Details of the Researcher

PHOTO

Masaaki Harada
Section
Graduate School of Information Sciences
Job title
Professor
Degree

  • 博士（理学）（岡山大学）

  • 修士（理学）（愛媛大学）

e-Rad No.
90292408

Committee Memberships 4

  • 日本数学会　地方区代議員

    2015/03 - 2016/02

  • 日本数学会　地方区代議員

    2015/03 - 2016/02

  • 日本数学会　全国区代議員

    2014/03 - 2015/02

  • 日本数学会　全国区代議員

    2014/03 - 2015/02

Professional Memberships 2

  • The Institute of Combinatorics and its Applications

  • 日本数学会

Research Interests 2

  • Combinatorics

  • Combinatorial coding theory

Research Areas 3

  • Natural sciences / Algebra / 代数的組合せ論

  • Natural sciences / Applied mathematics and statistics / 代数的符号理論

  • Natural sciences / Basic mathematics / 代数的符号理論

Awards 1

  1. Hall medal

    2005/03　The Institute of Combinatorics and its Applications

Papers 200

  1. A method for constructing quaternary Hermitian self-dual codes and an application to quantum codes Peer-reviewed

    Masaaki Harada

    Designs, Codes, and Cryptography　92　(10)　2927-2948　2024/10

    DOI： 10.1007/s10623-024-01421-x 　

    ISSN： 0925-1022

    eISSN： 1573-7586

  2. On the classification of skew Hadamard matrices of order 36 and related structures Peer-reviewed

    Makoto Araya, Masaaki Harada, Hadi Kharaghani, Ali Mohammadian, Behruz Tayfeh-Rezaie

    Designs, Codes, and Cryptography　92　(10)　3049-3062　2024/10

    DOI： 10.1007/s10623-024-01427-5 　

    ISSN： 0925-1022

    eISSN： 1573-7586

  3. IMPROVED LOWER BOUNDS FOR SELF-DUAL CODES OVER F<inf>11</inf>, F<inf>13</inf>, F<inf>17</inf>, F<inf>19</inf> AND F<inf>23</inf> Peer-reviewed

    T. Aaron Gulliver, Masaaki Harada

    Advances in Mathematics of Communications　18　(5)　1259-1265　2024/10

    DOI： 10.3934/amc.2022083 　

    ISSN： 1930-5346

    eISSN： 1930-5338

  4. Ternary Extremal Four-Negacirculant Self-Dual Codes Peer-reviewed

    Masaaki Harada, Keita Ishizuka, Hadi Kharaghani

    Graphs and Combinatorics　40　(3)　2024/05

    DOI： 10.1007/s00373-024-02788-3 　

    ISSN： 0911-0119

    eISSN： 1435-5914

  5. Hadamard matrices of order 36 formed by codewords in some ternary self-dual codes Peer-reviewed

    Masaaki Harada, Keita Ishizuka

    Discrete Mathematics　347　(1)　2024/01

    DOI： 10.1016/j.disc.2023.113661 　

    ISSN： 0012-365X

  6. Hadamard Matrices of Orders 60 and 64 with Automorphisms of Orders 29 and 31 Peer-reviewed

    Makoto Araya, Masaaki Harada, Vladimir D. Tonchev

    Electronic Journal of Combinatorics　31　(1)　2024

    DOI： 10.37236/12249 　

    eISSN： 1077-8926

  7. On the minimum weights of quaternary Hermitian LCD codes Peer-reviewed

    Makoto Araya, Masaaki Harada

    Cryptography and Communications　2024

    DOI： 10.1007/s12095-024-00733-y 　

    ISSN： 1936-2447

    eISSN： 1936-2455

  8. Characterizations of the Minimum Weights of LCD Codes of Large Dimensions Peer-reviewed

    Makoto Araya, Masaaki Harada, Keita Ishizuka, Yuto Tanaka

    IEEE Transactions on Information Theory　70　(12)　8758-8769　2024

    Publisher: Institute of Electrical and Electronics Engineers (IEEE)

    DOI： 10.1109/TIT.2024.3483218 　

    ISSN： 0018-9448

    eISSN： 1557-9654

  9. Some restrictions on the weight enumerators of near-extremal ternary self-dual codes and quaternary Hermitian self-dual codes

    Makoto Araya, Masaaki Harada

    Designs, Codes, and Cryptography　91　(5)　1813-1843　2023/05

    DOI： 10.1007/s10623-022-01172-7 　

    ISSN： 0925-1022

    eISSN： 1573-7586

  10. Construction of extremal Type II Z<inf>2k</inf>-codes Peer-reviewed

    Masaaki Harada

    Finite Fields and their Applications　87　2023/03

    DOI： 10.1016/j.ffa.2022.102154 　

    ISSN： 1071-5797

    eISSN： 1090-2465

  11. Self-dual codes over F<inf>5</inf> and s-extremal unimodular lattices Peer-reviewed

    Masaaki Harada

    Discrete Mathematics　346　(1)　2023/01

    DOI： 10.1016/j.disc.2022.113126 　

    ISSN： 0012-365X

  12. Hadamard matrices related to a certain series of ternary self-dual codes International-journal Peer-reviewed

    Makoto Araya, Masaaki Harada, Koji Momihara

    Designs, Codes and Cryptography　2022/10

    Publisher: Springer

    DOI： 10.1007/s10623-022-01127-y 　

  13. On the classification of quaternary optimal Hermitian LCD codes Peer-reviewed

    Makoto Araya, Masaaki Harada

    Cryptography and Communications　14　(4)　833-847　2022/07

    Publisher: Springer Science and Business Media LLC

    DOI： 10.1007/s12095-021-00552-5 　

    ISSN： 1936-2447

    eISSN： 1936-2455

  14. On the minimum weights of binary LCD codes and ternary LCD codes Peer-reviewed

    Makoto Araya, Masaaki Harada, Ken Saito

    Finite Fields and Their Applications　76　101925-101925　2021/12

    Publisher: Elsevier BV

    DOI： 10.1016/j.ffa.2021.101925 　

    ISSN： 1071-5797

  15. Construction of binary LCD codes, ternary LCD codes and quaternary Hermitian LCD codes Peer-reviewed

    Masaaki Harada

    Designs, Codes and Cryptography　89　(10)　2295-2312　2021/10

    Publisher: Springer Science and Business Media LLC

    DOI： 10.1007/s10623-021-00916-1 　

    ISSN： 0925-1022

    eISSN： 1573-7586

  16. On the existence of s -extremal singly even self-dual codes Peer-reviewed

    Masaaki Harada

    Discrete Mathematics, Algorithms and Applications　13　(2)　2021/04

    DOI： 10.1142/S1793830921500142 　

    ISSN： 1793-8309

    eISSN： 1793-8317

  17. Characterization and classification of optimal LCD codes Peer-reviewed

    Makoto Araya, Masaaki Harada, Ken Saito

    Designs, Codes, and Cryptography　2021

    DOI： 10.1007/s10623-020-00834-8 　

    ISSN： 0925-1022

    eISSN： 1573-7586

  18. Remark on subcodes of linear complementary dual codes Peer-reviewed

    Masaaki Harada, Ken Saito

    Information Processing Letters　159-160　2020/07

    DOI： 10.1016/j.ipl.2020.105963 　

    ISSN： 0020-0190

  19. Quaternary Hermitian Linear Complementary Dual Codes Peer-reviewed

    Makoto Araya, Masaaki Harada, Ken Saito

    IEEE Transactions on Information Theory　66　(5)　2751-2759　2020/05

    DOI： 10.1109/TIT.2019.2949040 　

    ISSN： 0018-9448

    eISSN： 1557-9654

  20. Construction of s-extremal optimal unimodular lattices in dimension 52 Peer-reviewed

    Masaaki Harada

    International Journal of Computer Mathematics: Computer Systems Theory　5　(2)　87-91　2020/04

    DOI： 10.1080/23799927.2020.1755367 　

    ISSN： 2379-9927

    eISSN： 2379-9935

  21. On the minimum weights of binary linear complementary dual codes Peer-reviewed

    Makoto Araya, Masaaki Harada

    Cryptography and Communications　12　(2)　285-300　2020/03/01

    DOI： 10.1007/s12095-019-00402-5 　

    ISSN： 1936-2447

    eISSN： 1936-2455

  22. New doubly even self-dual codes having minimum weight 20 Peer-reviewed

    Masaaki Harada

    Advances in Mathematics of Communications　14　(1)　89-96　2020/02

    DOI： 10.3934/amc.2020007 　

    ISSN： 1930-5346

    eISSN： 1930-5338

  23. On extremal double circulant self-dual codes of lengths 90–96 Peer-reviewed

    T. Aaron Gulliver, Masaaki Harada

    Applicable Algebra in Engineering, Communications and Computing　30　(5)　403-415　2019/11/01

    DOI： 10.1007/s00200-019-00381-3 　

    ISSN： 0938-1279

  24. Some optimal entanglement-assisted quantum codes constructed from quaternary Hermitian linear complementary dual codes Peer-reviewed

    Masaaki Harada

    International Journal of Quantum Information　17　(7)　2019/10/01

    DOI： 10.1142/S0219749919500539 　

    ISSN： 0219-7499

  25. Binary linear complementary dual codes Peer-reviewed

    Masaaki Harada, Ken Saito

    Cryptography and Communications　11　(4)　677-696　2019/07/15

    DOI： 10.1007/s12095-018-0319-0 　

    ISSN： 1936-2447

    eISSN： 1936-2455

  26. Singly even self-dual codes of length 24k + 10 and minimum weight 4k + 2 Peer-reviewed

    Masaaki Harada

    Cryptography and Communications　11　(4)　597-608　2019/07/15

    DOI： 10.1007/s12095-018-0303-8 　

    ISSN： 1936-2447

    eISSN： 1936-2455

  27. On the classification of linear complementary dual codes Peer-reviewed

    Makoto Araya, Masaaki Harada

    Discrete Mathematics　342　(1)　270-278　2019/01

    DOI： 10.1016/j.disc.2018.09.034 　

    ISSN： 0012-365X

  28. New quantum codes constructed from some self-dual additive F<inf>4</inf>-codes Peer-reviewed

    Masaaki Harada

    Information Processing Letters　138　35-38　2018/10

    DOI： 10.1016/j.ipl.2018.05.008 　

    ISSN： 0020-0190

  29. New extremal singly even self-dual codes of lengths 64 and 66 Peer-reviewed

    Damyan Anev, Masaaki Harada, Nikolay Yankov

    J. Algebra Comb. Discrete Struct. Appl.　5　143-151　2018/09

  30. Some restrictions on weight enumerators of singly even self-dual codes II Peer-reviewed

    Masaaki Harada, Akihiro Munemasa

    Interdiscip. Inform. Sci.　24　77-85　2018/06

  31. Binary extremal self-dual codes of length 60 and related codes Peer-reviewed

    Masaaki Harada

    Designs, Codes, and Cryptography　86　(5)　1085-1094　2018/05/01

    DOI： 10.1007/s10623-017-0380-2 　

    ISSN： 0925-1022

    eISSN： 1573-7586

  32. Nonexistence of certain singly even self-dual codes with minimal shadow Peer-reviewed

    Stefka Bouyuklieva, Masaaki Harada

    Electronic Journal of Combinatorics　25　(1)　P1.13　2018/01/25

    DOI： 10.37236/7155 　

    eISSN： 1077-8926

  33. Singly even self-dual codes constructed from Hadamard matrices of order 28 Peer-reviewed

    Masaaki Harada, Ken Saito

    Australasian Journal of Combinatorics　70　(2)　288-296　2018

    ISSN： 1034-4942

    eISSN： 2202-3518

  34. Architecture of an FPGA-based heterogeneous system for code-search problems Peer-reviewed

    Yuki Hiradate, Hasitha Muthumala Waidyasooriya, Masanori Hariyama, Masaaki Harada

    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)　10776 LNCS　146-155　2018

    Publisher: Springer Verlag

    DOI： 10.1007/978-3-319-69953-0_9 　

    ISSN： 0302-9743

    eISSN： 1611-3349

  35. Ternary maximal self-orthogonal codes of lengths 21, 22 and 23 Peer-reviewed

    Makoto Araya, Masaaki Harada, Yuichi Suzuki

    J. Algebra Comb. Discrete Struct. Appl.　5　1-4　2017/12

  36. On s-extremal singly even self-dual [24 kappa+8,121 kappa+4, 4 kappa+2] codes Peer-reviewed

    Masaaki Harada, Akihiro Munemasa

    FINITE FIELDS AND THEIR APPLICATIONS　48　306-317　2017/11

    DOI： 10.1016/j.ffa.2017.08.008 　

    ISSN： 1071-5797

    eISSN： 1090-2465

  37. Performance of ternary double circulant, double twistulant, and self-dual codes Peer-reviewed

    T. Aaron Gulliver, Masaaki Harada

    APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING　28　(5)　409-424　2017/11

    DOI： 10.1007/s00200-017-0312-4 　

    ISSN： 0938-1279

    eISSN： 1432-0622

  38. ON THE PERFORMANCE OF OPTIMAL DOUBLE CIRCULANT EVEN CODES Peer-reviewed

    T. Aaron Gulliver, Masaaki Harada

    ADVANCES IN MATHEMATICS OF COMMUNICATIONS　11　(4)　767-775　2017/11

    DOI： 10.3934/amc.2017056 　

    ISSN： 1930-5346

    eISSN： 1930-5338

  39. ON THE CLASSIFICATION OF Z(4)-CODES Peer-reviewed

    Makoto Araya, Masaaki Harada, Hiroki Ito, Ken Saito

    ADVANCES IN MATHEMATICS OF COMMUNICATIONS　11　(4)　747-756　2017/11

    DOI： 10.3934/amc.2017054 　

    ISSN： 1930-5346

    eISSN： 1930-5338

  40. Self-dual codes and the non-existence of a quasi-symmetric 2-(37,9,8) design with intersection numbers 1 and 3 Peer-reviewed

    Masaaki Harada, Akihiro Munemasa, Vladimir D. Tonchev

    J. Combin. Designs　25　469-476　2017/08

  41. Extremal Type II Z4-codes constructed from binary doubly even self-dual codes of length 40 Peer-reviewed

    Masaaki Harada

    Discrete Math.　340　2466-2468　2017/07

  42. A note on the fertilization success of the first male during successive mating in the Japanese rhinoceros beetle Trypoxylus dichotomus septentrionalis Peer-reviewed

    Masaaki Harada, Naoyuki Fujiyama

    J. Insect Behavior　30　231-236　2017/06

  43. Quasi-unbiased hadamard matrices and weakly unbiased hadamard matrices: A coding-theoretic approach Peer-reviewed

    Makoto Araya, Masaaki Harada, Sho Suda

    Mathematics of Computation　86　(304)　951-984　2017

    Publisher: American Mathematical Society

    DOI： 10.1090/mcom/3122 　

    ISSN： 0025-5718

  44. New self-dual additive F4-codes constructed from circulant graphs Peer-reviewed

    Markus Grassl, Masaaki Harada

    Discrete Math　340　399-403　2017/01

  45. On the classification of self-dual [20,10,9] codes over GF(7) Peer-reviewed

    Masaaki Harada, Akihiro Munemasa

    FINITE FIELDS AND THEIR APPLICATIONS　42　57-66　2016/11

    DOI： 10.1016/j.ffa.2016.07.004 　

    ISSN： 1071-5797

    eISSN： 1090-2465

  46. NOTE ON THE RESIDUE CODES OF SELF-DUAL Z(4)-CODES HAVING LARGE MINIMUM LEE WEIGHTS Peer-reviewed

    Masaaki Harada

    ADVANCES IN MATHEMATICS OF COMMUNICATIONS　10　(4)　695-706　2016/11

    DOI： 10.3934/ame.2016035 　

    ISSN： 1930-5346

    eISSN： 1930-5338

  47. On the classification of self-dual Zk-codes II Peer-reviewed

    Masaaki Harada, Akihiro Munemasa

    Interdiscip. Inform. Sci.　22　(1)　81-85　2016/11

    Publisher: Graduate School of Information Sciences, Tohoku University

    DOI： 10.4036/iis.2015.R.01 　

    ISSN： 1347-6157

    More details Close

    In this short note, we report the classification of self-dual \mathbb{Z}k-codes of length n for k ≤ 24 and n ≤ 9.

  48. THE WEIGHT DISTRIBUTION OF THE SELF-DUAL [128,64] POLARITY DESIGN CODE Peer-reviewed

    Masaaki Harada, Ethan Novak, Vladimir D. Tonchev

    ADVANCES IN MATHEMATICS OF COMMUNICATIONS　10　(3)　643-648　2016/08

    DOI： 10.3934/amc.2016032 　

    ISSN： 1930-5346

    eISSN： 1930-5338

  49. On binary codes related to mutually quasi-unbiased weighing matrices Peer-reviewed

    Masaaki Harada, Sho Suda

    Australasian J. Combin.　66　10-22　2016/08

  50. Supplementary difference sets related to a certain class of complex spherical 2-code Peer-reviewed

    Makoto Araya, Masaaki Harada, Sho Suda

    Australasian J. Combin.　65　71-83　2016/04

  51. On the classification of certain ternary codes of length 12 Peer-reviewed

    Makoto Araya, Masaaki Harada

    HIROSHIMA MATHEMATICAL JOURNAL　46　(1)　87-96　2016/03

    ISSN： 0018-2079

  52. On a 5-design related to a putative extremal doubly even self-dual code of length a multiple of 24 Peer-reviewed

    Masaaki Harada

    DESIGNS CODES AND CRYPTOGRAPHY　76　(3)　373-384　2015/09

    DOI： 10.1007/s10623-014-9963-3 　

    ISSN： 0925-1022

    eISSN： 1573-7586

  53. Extremal Type I Z(k)-Codes and k-Frames of Odd Unimodular Lattices Peer-reviewed

    Masaaki Harada

    IEEE TRANSACTIONS ON INFORMATION THEORY　61　(1)　72-81　2015/01

    DOI： 10.1109/TIT.2014.2368563 　

    ISSN： 0018-9448

    eISSN： 1557-9654

  54. Extremal unimodular lattices in dimension 36 Peer-reviewed

    Masaaki Harada

    International J. Combin.　2014　Article ID 792471　2014/11

  55. On the classification of extremal doubly even self-dual codes with 2-transitive automorphism groups Peer-reviewed

    Naoki Chigira, Masaaki Harada, Masaaki Kitazume

    DESIGNS CODES AND CRYPTOGRAPHY　73　(1)　33-35　2014/10

    DOI： 10.1007/s10623-013-9807-6 　

    ISSN： 0925-1022

    eISSN： 1573-7586

  56. On the existence of extremal type II ℤ2k-codes Peer-reviewed

    Masaaki Harada, Tsuyoshi Miezaki

    Mathematics of Computation　83　(287)　1427-1446　2014/05

    DOI： 10.1090/S0025-5718-2013-02750-0 　

    ISSN： 0025-5718

  57. There is no [21,5,14] code over F-5 Peer-reviewed

    Makoto Araya, Masaaki Harada

    DISCRETE MATHEMATICS　313　(24)　2872-2874　2013/12

    DOI： 10.1016/j.disc.2013.08.027 　

    ISSN： 0012-365X

    eISSN： 1872-681X

  58. A complete classification of doubly even self-dual codes of length 40 Peer-reviewed

    Koichi Betsumiya, Masaaki Harada, Akihiro Munemasa

    Electronic J. Combin　19　P18-16　2013/07

  59. Residue codes of extremal Type II Z(4)-codes and the moonshine vertex operator algebra Peer-reviewed

    Masaaki Harada, Ching Hung Lam, Akihiro Munemasa

    MATHEMATISCHE ZEITSCHRIFT　274　(1-2)　685-700　2013/06

    DOI： 10.1007/s00209-012-1091-z 　

    ISSN： 0025-5874

  60. Some extremal self-dual codes and unimodular lattices in dimension 40 Peer-reviewed

    Stefka Bouyuklieva, Iliya Bouyukliev, Masaaki Harada

    FINITE FIELDS AND THEIR APPLICATIONS　21　67-83　2013/05

    DOI： 10.1016/j.ffa.2013.01.009 　

    ISSN： 1071-5797

  61. Optimal self-dual Z(4)-codes and a unimodular lattice in dimension 41 Peer-reviewed

    Masaaki Harada

    FINITE FIELDS AND THEIR APPLICATIONS　18　(3)　529-536　2012/05

    DOI： 10.1016/j.ffa.2011.11.004 　

    ISSN： 1071-5797

  62. CLASSIFICATION OF SELF-DUAL CODES OF LENGTH 36 Peer-reviewed

    Masaaki Harada, Akihiro Munemasa

    ADVANCES IN MATHEMATICS OF COMMUNICATIONS　6　(2)　229-235　2012/05

    DOI： 10.3934/amc.2012.6.229 　

    ISSN： 1930-5346

  63. On the classification of weighing matrices and self-orthogonal codes Peer-reviewed

    Masaaki Harada, Akihiro Munemasa

    JOURNAL OF COMBINATORIAL DESIGNS　20　(1)　40-57　2012/01

    DOI： 10.1002/jcd.20295 　

    ISSN： 1063-8539

  64. An optimal odd unimodular lattice in dimension 72 Peer-reviewed

    Masaaki Harada, Tsuyoshi Miezaki

    ARCHIV DER MATHEMATIK　97　(6)　529-533　2011/12

    DOI： 10.1007/s00013-011-0333-3 　

    ISSN： 0003-889X

  65. On the residue codes of extremal Type II Z(4)-codes of lengths 32 and 40 Peer-reviewed

    Masaaki Harada

    DISCRETE MATHEMATICS　311　(20)　2148-2157　2011/10

    DOI： 10.1016/j.disc.2011.06.022 　

    ISSN： 0012-365X

  66. CONSTRUCTION OF SOME UNIMODULAR LATTICES WITH LONG SHADOWS Peer-reviewed

    Masaaki Harada

    INTERNATIONAL JOURNAL OF NUMBER THEORY　7　(5)　1345-1358　2011/08

    DOI： 10.1142/S1793042111004794 　

    ISSN： 1793-0421

  67. Classification of Quaternary Hermitian Self-Dual Codes of Length 20 Peer-reviewed

    Masaaki Harada, Akihiro Munemasa

    IEEE TRANSACTIONS ON INFORMATION THEORY　57　(6)　3758-3762　2011/06

    DOI： 10.1109/TIT.2011.2134330 　

    ISSN： 0018-9448

  68. Hadamard matrices of order 32 and extremal ternary self-dual codes Peer-reviewed

    Koichi Betsumiya, Masaaki Harada, Hiroshi Kimura

    DESIGNS CODES AND CRYPTOGRAPHY　58　(2)　203-214　2011/02

    DOI： 10.1007/s10623-010-9403-y 　

    ISSN： 0925-1022

  69. An upper bound on the minimum weight of Type II Z(2k)-codes Peer-reviewed

    Masaaki Harada, Tsuyoshi Miezaki

    JOURNAL OF COMBINATORIAL THEORY SERIES A　118　(1)　190-196　2011/01

    DOI： 10.1016/j.jcta.2010.02.007 　

    ISSN： 0097-3165

  70. Classification of Generalized Hadamard Matrices H(6,3) and Quaternary Hermitian Self-Dual Codes of Length 18 Peer-reviewed

    Masaaki Harada, Clement Lam, Akihiro Munemasa, Vladimir D. Tonchev

    ELECTRONIC JOURNAL OF COMBINATORICS　17　(1)　R171　2010/12

    ISSN： 1077-8926

  71. Extremal Type II Z(4)-codes of lengths 56 and 64 Peer-reviewed

    Masaaki Harada

    JOURNAL OF COMBINATORIAL THEORY SERIES A　117　(8)　1285-1288　2010/11

    DOI： 10.1016/j.jcta.2009.09.003 　

    ISSN： 0097-3165

  72. Mutually Disjoint Designs and New 5-Designs Derived from Groups and Codes Peer-reviewed

    Makoto Araya, Masaaki Harada, Vladimir D. Tonchev, Alfred Wassermann

    JOURNAL OF COMBINATORIAL DESIGNS　18　(4)　305-317　2010/07

    DOI： 10.1002/jcd.20251 　

    ISSN： 1063-8539

  73. New Binary Singly Even Self-Dual Codes Peer-reviewed

    Masaaki Harada, Michael Kiermaier, Alfred Wassermann, Radinka Yorgova

    IEEE TRANSACTIONS ON INFORMATION THEORY　56　(4)　1612-1617　2010/04

    DOI： 10.1109/TIT.2010.2040967 　

    ISSN： 0018-9448

  74. Mutually Disjoint Steiner Systems S(5,8,24) and 5-(24,12,48) Designs Peer-reviewed

    Makoto Araya, Masaaki Harada

    ELECTRONIC JOURNAL OF COMBINATORICS　17　(1)　N1　2010/01

    ISSN： 1077-8926

  75. MDS self-dual codes of lengths 16 and 18 Peer-reviewed

    T. Aaron Gulliver, Masaaki Harada

    Inter. J. Inform. and Coding Theory　1　208-213　2010

  76. NEW EXTREMAL FORMALLY SELF-DUAL EVEN CODES OF LENGTH 30 Peer-reviewed

    Masaaki Harada, Katsushi Waki

    ADVANCES IN MATHEMATICS OF COMMUNICATIONS　3　(4)　311-316　2009/11

    DOI： 10.3934/amc.2009.3.311 　

    ISSN： 1930-5346

  77. There exists no self-dual [24,12,10] code over F(5) Peer-reviewed

    Masaaki Harada, Akihiro Munemasa

    DESIGNS CODES AND CRYPTOGRAPHY　52　(1)　125-127　2009/07

    DOI： 10.1007/s10623-009-9271-5 　

    ISSN： 0925-1022

  78. CLASSIFICATION OF TERNARY EXTREMAL SELF-DUAL CODES OF LENGTH 28 Peer-reviewed

    Masaaki Harada, Akihiro Munemasa, Boris Venkov

    MATHEMATICS OF COMPUTATION　78　(267)　1787-1796　2009/07

    DOI： 10.1090/S0025-5718-08-02194-7 　

    ISSN： 0025-5718

  79. A complete classification of ternary self-dual codes of length 24 Peer-reviewed

    Masaaki Harada, Akihiro Munemasa

    JOURNAL OF COMBINATORIAL THEORY SERIES A　116　(5)　1063-1072　2009/07

    DOI： 10.1016/j.jcta.2008.11.011 　

    ISSN： 0097-3165

  80. On the existence of frames of the Niemeier lattices and self-dual codes over F-p Peer-reviewed

    Masaaki Harada

    JOURNAL OF ALGEBRA　321　(8)　2345-2352　2009/04

    DOI： 10.1016/j.jalgebra.2009.02.001 　

    ISSN： 0021-8693

  81. On the Classification of Self-dual ZZ(k)-Codes Peer-reviewed

    Masaaki Harada, Akihiro Munemasa

    CRYPTOGRAPHY AND CODING, PROCEEDINGS　5921　78-+　2009

    DOI： 10.1007/978-3-642-10868-6_6 　

    ISSN： 0302-9743

  82. Classification of circulant D-optimal designs of orders 62 and 74 Peer-reviewed

    Makoto Araya, Masaaki Harada

    J. Statis. Appl.　4　301-312　2009

  83. Small non-embeddable quasi-derived designs Peer-reviewed

    Masaaki Harada, Hiroki Miyabayashi

    JOURNAL OF COMBINATORIAL DESIGNS　16　(5)　364-372　2008/09

    DOI： 10.1002/jcd.20168 　

    ISSN： 1063-8539

  84. An extremal doubly even self-dual code of length 112 Peer-reviewed

    Masaaki Harada

    ELECTRONIC JOURNAL OF COMBINATORICS　15　(1)　N33　2008/08

    ISSN： 1077-8926

  85. Determination of weight enumerators of binary extremal self-dual [42,21,8] codes Peer-reviewed

    Stefka Bouyuklieva, Masaaki Harada, Akihiro Munemasa

    FINITE FIELDS AND THEIR APPLICATIONS　14　(1)　177-187　2008/01

    DOI： 10.1016/j.ffa.2006.11.004 　

    ISSN： 1071-5797

  86. On double circulant doubly even self-dual [72,36,12] codes and their neighbors Peer-reviewed

    T. Aaron Gulliver, Masaaki Harada

    Australasian J. Combin.　40　137-144　2008

  87. New nonbinary self-dual codes Peer-reviewed

    T. Aaron Gulliver, Masaaki Harada

    IEEE TRANSACTIONS ON INFORMATION THEORY　54　(1)　415-417　2008/01

    DOI： 10.1109/TIT.2007.911265 　

    ISSN： 0018-9448

  88. Some self-dual codes invariant under the Hall-Janko group Peer-reviewed

    Naoki Chigira, Masaaki Harada, Masaaki Kitazume

    JOURNAL OF ALGEBRA　316　(2)　578-590　2007/10

    DOI： 10.1016/j.jalgebra.2007.05.015 　

    ISSN： 0021-8693

  89. Extremal ternary self-dual codes constructed from negacirculant matrices Peer-reviewed

    Masaaki Harada, W. Holzmann, H. Kharaghani, M. Khorvash

    GRAPHS AND COMBINATORICS　23　(4)　401-417　2007/08

    DOI： 10.1007/s00373-007-0731-2 　

    ISSN： 0911-0119

  90. An extremal singly even self-dual code of length 88 Peer-reviewed

    Masaaki Harada, Takuji Nishimura

    ADVANCES IN MATHEMATICS OF COMMUNICATIONS　1　(2)　261-267　2007/05

    ISSN： 1930-5346

  91. On the covering radii of extremal doubly even self-dual codes Peer-reviewed

    Masaaki Harada, Akihiro Munemasa

    ADVANCES IN MATHEMATICS OF COMMUNICATIONS　1　(2)　251-256　2007/05

    ISSN： 1930-5346

  92. Double circulant and quasi-twisted self-dual codes over F-5 and F-7 Peer-reviewed

    T. Aaron Gulliver, Masaaki Harada, Hiroki Miyabayashi

    ADVANCES IN MATHEMATICS OF COMMUNICATIONS　1　(2)　223-238　2007/05

    ISSN： 1930-5346

  93. Permutation groups and binary self-orthogonal codes Peer-reviewed

    Naoki Chigira, Masaaki Harada, Masaaki Kitazume

    JOURNAL OF ALGEBRA　309　(2)　610-621　2007/03

    DOI： 10.1016/j.jalgebra.2006.06.001 　

    ISSN： 0021-8693

  94. Extremal self-dual codes of length 64 through neighbors and covering radii Peer-reviewed

    Naoki Chigira, Masaaki Harada, Masaaki Kitazume

    DESIGNS CODES AND CRYPTOGRAPHY　42　(1)　93-101　2007/01

    DOI： 10.1007/s10623-006-9018-5 　

    ISSN： 0925-1022

  95. On the complete coset weight distributions of extremal formally self-dual even codes Peer-reviewed

    Masaaki Harada

    Bull. Yamagata Univ. (Natural Sci.)　16　71-79　2007

  96. New extremal self-dual codes of length 66 Peer-reviewed

    Masaaki Harada, Takuji Nishimura, Radinka Yorgova

    Mathematica Balkanica　21　113-121　2007

  97. Optimal double circulant self-dual codes over F4 II Peer-reviewed

    T. Aaron Gulliver, Masaaki Harada, Hiroki Miyabayash

    Australasian J. Combin.　39　163-174　2007

  98. Classification of extremal double circulant self-dual codes of lengths 74-88 Peer-reviewed

    T. Aaron Gulliver, Masaaki Harada

    DISCRETE MATHEMATICS　306　(17)　2064-2072　2006/09

    DOI： 10.1016/j.disc.2006.05.004 　

    ISSN： 0012-365X

  99. Some restrictions on weight enumerators of singly even self-dual codes Peer-reviewed

    M Harada, A Munemasa

    IEEE TRANSACTIONS ON INFORMATION THEORY　52　(3)　1266-1269　2006/03

    DOI： 10.1109/TIT.2005.864416 　

    ISSN： 0018-9448

  100. Self-orthogonal 3-(56,12,65) designs and extremal doubly-even self-dual codes of length 56 Peer-reviewed

    M Harada

    DESIGNS CODES AND CRYPTOGRAPHY　38　(1)　5-16　2006/01

    DOI： 10.1007/s10623-004-5657-6 　

    ISSN： 0925-1022

  101. Orthogonal designs and MDS self-dual codes Peer-reviewed

    Masaaki Harada, Hadi Kharaghani

    Australasian J. Combin.　35　57-67　2006

  102. Near-extremal formally self-dual even codes of lengths 24 and 32 Peer-reviewed

    TA Gulliver, M Harada, T Nishimura, PRJ Ostergard

    DESIGNS CODES AND CRYPTOGRAPHY　37　(3)　465-471　2005/12

    DOI： 10.1007/s10623-004-4037-6 　

    ISSN： 0925-1022

  103. Remark on a 5-design related to a putative extremal doubly-even self-dual [96,48,20] code Peer-reviewed

    M Harada

    DESIGNS CODES AND CRYPTOGRAPHY　37　(2)　355-358　2005/11

    DOI： 10.1007/s10623-004-3997-x 　

    ISSN： 0925-1022

  104. On some self-dual codes and unimodular lattices in dimension 48 Peer-reviewed

    M Harada, M Kitazume, A Munemasa, B Venkov

    EUROPEAN JOURNAL OF COMBINATORICS　26　(5)　543-557　2005/07

    DOI： 10.1016/j.ejc.2004.06.013 　

    ISSN： 0195-6698

  105. A characterization of designs related to an extremal doubly-even self-dual code of length 48 Peer-reviewed

    Masaaki Harada, Akihiro Munemasa, Vladimir D. Tonchev

    ANNALS OF COMBINATORICS　9　(2)　189-198　2005/07

    DOI： 10.1007/s00026-005-0250-x 　

    ISSN： 0218-0006

  106. On the complete coset weight distribution of the extremal self-dual[46,23,10] code Peer-reviewed

    M Harada, T Nishimura

    IEEE TRANSACTIONS ON INFORMATION THEORY　51　(7)　2700-2702　2005/07

    DOI： 10.1109/TIT.2005.850156 　

    ISSN： 0018-9448

  107. On the self-dual F-5-codes constructed from Hadamard matrices of order 24 Peer-reviewed

    M Harada

    JOURNAL OF COMBINATORIAL DESIGNS　13　(2)　152-156　2005

    DOI： 10.1002/jcd.20021 　

    ISSN： 1063-8539

  108. Symmetric (4,4)-nets and generalized Hadamard matrices over groups of order 4 Peer-reviewed

    M Harada, C Lam, VD Tonchev

    DESIGNS CODES AND CRYPTOGRAPHY　34　(1)　71-87　2005/01

    DOI： 10.1007/s10623-003-4195-y 　

    ISSN： 0925-1022

  109. Orthogonal designs, self-dual codes, and the leech lattice Peer-reviewed

    M Harada, H Kharaghani

    JOURNAL OF COMBINATORIAL DESIGNS　13　(3)　184-194　2005

    DOI： 10.1002/jcd.20046 　

    ISSN： 1063-8539

  110. Extremal self-dual codes over Z6, Z8 and Z10 Peer-reviewed

    T. Aaron Gulliver, Masaaki Harada

    AKCE Intern. J. Graphs Combin.　2　11-24　2005

  111. On the covering radius of ternary extremal self-dual codes Peer-reviewed

    M Harada, M Ozeki, K Tanabe

    DESIGNS CODES AND CRYPTOGRAPHY　33　(2)　149-158　2004/09

    DOI： 10.1023/B:DESI.0000035468.86695.40 　

    ISSN： 0925-1022

  112. On a 5-design related to an extremal doubly even self-dual code of length 72 Peer-reviewed

    M Harada, M Kitazume, A Munemasa

    JOURNAL OF COMBINATORIAL THEORY SERIES A　107　(1)　143-146　2004/07

    DOI： 10.1016/j.jcta.2004.03.005 　

    ISSN： 0097-3165

  113. MDS codes over F-9 related to the temary Golay code Peer-reviewed

    M Araya, M Harada

    DISCRETE MATHEMATICS　282　(1-3)　233-237　2004/05

    DOI： 10.1016/j.disc.2003.11.012 　

    ISSN： 0012-365X

  114. Extremal self-dual [40,20,8] codes with covering radius 7 Peer-reviewed

    M Harada, A Munemasa, K Tanabe

    FINITE FIELDS AND THEIR APPLICATIONS　10　(2)　183-197　2004/04

    DOI： 10.1016/j.ffa.2003.08.001 　

    ISSN： 1071-5797

  115. Optimal Self-Dual Codes Over double struct F sign2 × double struct F sign2 With Respect to the Hamming Weight Peer-reviewed

    Koichi Betsumiya, Masaaki Harada

    IEEE Transactions on Information Theory　50　(2)　356-410　2004/02

    DOI： 10.1109/TIT.2003.822576 　

    ISSN： 0018-9448

  116. On the minimum weight of codes over F-5 constructed from certain conference matrices Peer-reviewed

    TA Gulliver, M Harada

    DESIGNS CODES AND CRYPTOGRAPHY　31　(2)　139-145　2004/02

    DOI： 10.1023/B:DESI.0000012442.78414.e4 　

    ISSN： 0925-1022

  117. Optimal self-dual codes over F-2 x F-2 with respect to the hamming weight Peer-reviewed

    K Betsumiya, M Harada

    IEEE TRANSACTIONS ON INFORMATION THEORY　50　(2)　356-358　2004/02

    DOI： 10.1109/TIT.2003.822579 　

    ISSN： 0018-9448

  118. Some Hadamard matrices of order 32 and their binary codes Peer-reviewed

    M Araya, M Harada, H Kharaghani

    JOURNAL OF COMBINATORIAL DESIGNS　12　(2)　142-146　2004

    DOI： 10.1002/jcd.10057 　

    ISSN： 1063-8539

  119. Some extremal self-dual codes with an automorphism of order 7 Peer-reviewed

    R Dontcheva, M Harada

    APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING　14　(2)　75-79　2003/08

    DOI： 10.1007/s00200-003-0126-4 　

    ISSN： 0938-1279

  120. Formally self-dual codes related to Type II codes Peer-reviewed

    K Betsumiya, M Harada

    APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING　14　(2)　81-88　2003/08

    DOI： 10.1007/s00200-003-0127-3 　

    ISSN： 0938-1279

  121. Extremal doubly-even [80,40,16] codes with an automorphism of order 19 Peer-reviewed

    R Dontcheva, M Harada

    FINITE FIELDS AND THEIR APPLICATIONS　9　(2)　157-167　2003/04

    DOI： 10.1016/S1071-5797(02)00018-7 　

    ISSN： 1071-5797

  122. Self-orthogonal codes from symmetric designs with fixed-point-free automorphisms Peer-reviewed

    M Harada, VD Tonchev

    DISCRETE MATHEMATICS　264　(1-3)　81-90　2003/03

    DOI： 10.1016/S0012-365X(02)00553-8 　

    ISSN： 0012-365X

  123. Extremal self-dual [50,25,10] codes with automorphisms of order 3 and quasi-symmetric 2-(49,9,6) designs Peer-reviewed

    S Bouyuklieva, M Harada

    DESIGNS CODES AND CRYPTOGRAPHY　28　(2)　163-169　2003/03

    DOI： 10.1023/A:1022588407585 　

    ISSN： 0925-1022

  124. Extremal self-dual codes over F-2 x F-2 Peer-reviewed

    K Betsumiya, TA Gulliver, M Harada

    DESIGNS CODES AND CRYPTOGRAPHY　28　(2)　171-186　2003/03

    DOI： 10.1023/A:1022540524423 　

    ISSN： 0925-1022

  125. On self-dual codes over some prime fields Peer-reviewed

    K Betsumiya, S Georgiou, TA Gullivere, M Harada, C Koukouvinos

    DISCRETE MATHEMATICS　262　(1-3)　37-58　2003/02

    DOI： 10.1016/S0012-365X(02)00520-4 　

    ISSN： 0012-365X

  126. Construction of new extremal self-dual codes Peer-reviewed

    TA Gulliver, M Harada, JL Kim

    DISCRETE MATHEMATICS　263　(1-3)　81-91　2003/02

    DOI： 10.1016/S0012-365X(02)00570-8 　

    ISSN： 0012-365X

  127. Extremal odd unimodular lattices in dimensions 44, 46 and 47 Peer-reviewed

    Masaaki Harada

    Hokkaido Math. J　32　153-159　2003

  128. On the classification of self-dual codes over F-5 Peer-reviewed

    M Harada, PRJ Ostergard

    GRAPHS AND COMBINATORICS　19　(2)　203-214　2003

    DOI： 10.1007/s00373-002-0502-z 　

    ISSN： 0911-0119

  129. On Hadamard matrices of order 2(p+1) with an automorphism of odd prime order p Peer-reviewed

    DB Dalan, M Harada, A Munemasa

    JOURNAL OF COMBINATORIAL DESIGNS　11　(5)　367-380　2003

    DOI： 10.1002/jcd.10052 　

    ISSN： 1063-8539

  130. Type II codes over F-2+uF(2) and applications to Hermitian modular forms Peer-reviewed

    E Bannai, M Harada, T Ibukiyama, A Munemasa, M Oura

    ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG　73　13-42　2003

    DOI： 10.1007/BF02941267 　

    ISSN： 0025-5858

  131. Self-dual and maximal self-orthogonal codes over F-7 Peer-reviewed

    M Harada, PRJ Ostergard

    DISCRETE MATHEMATICS　256　(1-2)　471-477　2002/09

    ISSN： 0012-365X

  132. Ternary code construction of unimodular lattices and self-dual codes over Z(6) Peer-reviewed

    M Harada, M Kitazume, M Ozeki

    JOURNAL OF ALGEBRAIC COMBINATORICS　16　(2)　209-223　2002/09

    DOI： 10.1023/A:1021185314365 　

    ISSN： 0925-9899

  133. New extremal self-dual codes of length 62 and related extremal self-dual codes Peer-reviewed

    R Dontcheva, M Harada

    IEEE TRANSACTIONS ON INFORMATION THEORY　48　(7)　2060-2064　2002/07

    DOI： 10.1109/TIT.2002.1013144 　

    ISSN： 0018-9448

  134. Z(6)-code constructions of the Leech lattice and the Niemeier lattices Peer-reviewed

    M Harada, M Kitazume

    EUROPEAN JOURNAL OF COMBINATORICS　23　(5)　573-581　2002/07

    DOI： 10.1006/eujc.2002.0557 　

    ISSN： 0195-6698

  135. On type IV self-dual codes over Z(4) Peer-reviewed

    S Bouyuklieva, M Harada

    DISCRETE MATHEMATICS　247　(1-3)　25-50　2002/03

    ISSN： 0012-365X

  136. Orthogonal designs and Type II codes over Z(2k) Peer-reviewed

    S Georgiou, M Harada, C Koukouvinos

    DESIGNS CODES AND CRYPTOGRAPHY　25　(2)　163-174　2002/02

    ISSN： 0925-1022

  137. Self-dual Z(4)-codes and Hadamard matrices Peer-reviewed

    M Harada

    DISCRETE MATHEMATICS　245　(1-3)　273-278　2002/02

    ISSN： 0012-365X

  138. A quasi-symmetric 2-(49,9,6) design Peer-reviewed

    M Harada, A Munemasa

    JOURNAL OF COMBINATORIAL DESIGNS　10　(3)　173-179　2002

    DOI： 10.1002/jcd.10007 　

    ISSN： 1063-8539

  139. Classification of extremal formally self-dual even codes of length 22 Peer-reviewed

    M Harada, PRJ Ostergard

    GRAPHS AND COMBINATORICS　18　(3)　507-516　2002

    DOI： 10.1007/s003730200037 　

    ISSN： 0911-0119

  140. Shadow codes over Z(4) Peer-reviewed

    ST Dougherty, M Harada, P Sole

    FINITE FIELDS AND THEIR APPLICATIONS　7　(4)　507-529　2001/10

    DOI： 10.1006/ffta.2000.0312 　

    ISSN： 1071-5797

  141. On type II codes over F-4 Peer-reviewed

    K Betsumiya, TA Gulliver, M Harada, A Munemasa

    IEEE TRANSACTIONS ON INFORMATION THEORY　47　(6)　2242-2248　2001/09

    ISSN： 0018-9448

  142. An extremal ternary self-dual [28,14,9] code with a trivial automorphism group Peer-reviewed

    M Harada

    DISCRETE MATHEMATICS　239　(1-3)　121-125　2001/08

    DOI： 10.1016/S0012-365X(01)00041-3 　

    ISSN： 0012-365X

  143. Orthogonal frames in the leech lattice and a type II code over Z(22) Peer-reviewed

    TA Gulliver, M Harada

    JOURNAL OF COMBINATORIAL THEORY SERIES A　95　(1)　185-188　2001/07

    DOI： 10.1006/jcta.2000.3159 　

    ISSN： 0097-3165

  144. Binary optimal odd formally self-dual codes Peer-reviewed

    K Betsumiya, M Harada

    DESIGNS CODES AND CRYPTOGRAPHY　23　(1)　11-21　2001/05

    DOI： 10.1023/A:1011203416769 　

    ISSN： 0925-1022

  145. Note on the g-fold joint weight enumerators of self-dual codes over Z(k) Peer-reviewed

    ST Dougherty, M Harada, M Oura

    APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING　11　(6)　437-445　2001/05

    ISSN： 0938-1279

  146. Codes over F-3 + uF(3) and improvements to the bounds on ternary linear codes Peer-reviewed

    TA Gulliver, M Harada

    DESIGNS CODES AND CRYPTOGRAPHY　22　(1)　89-96　2001/01

    DOI： 10.1023/A:1008355310919 　

    ISSN： 0925-1022

  147. Classification of formally self-dual even codes of lengths up to 16 Peer-reviewed

    K Betsumiya, M Harada

    DESIGNS CODES AND CRYPTOGRAPHY　23　(3)　325-332　2001

    DOI： 10.1023/A:1011223128089 　

    ISSN： 0925-1022

  148. Optimal double circulant Z4-codes Peer-reviewed

    T. Aaron Gulliver, Masaaki Harada

    Lecture Notes in Comput. Sci.　2227　122-128　2001

  149. Type II codes over Peer-reviewed

    Koichi Betsumiya, Masaaki Harada, Akihiro Munemasa

    Lecture Notes in Comput. Sci.　2227　102-111　2001

  150. Isodual codes over Z(2k) and isodual lattices Peer-reviewed

    C Bachoc, TA Gulliver, M Harada

    JOURNAL OF ALGEBRAIC COMBINATORICS　12　(3)　223-240　2000/11

    ISSN： 0925-9899

  151. On the existence of extremal Type II codes over Z(6) Peer-reviewed

    M Harada

    DISCRETE MATHEMATICS　223　(1-3)　373-378　2000/08

    ISSN： 0012-365X

  152. Classification of type IV self-dual Z(4)-Codes of length 16 Peer-reviewed

    M Harada, A Munemasa

    FINITE FIELDS AND THEIR APPLICATIONS　6　(3)　244-254　2000/07

    ISSN： 1071-5797

  153. Double circulant self-dual codes over GF(5) Peer-reviewed

    TA Gulliver, M Harada

    ARS COMBINATORIA　56　3-13　2000/07

    ISSN： 0381-7032

  154. Z(4)-code constructions for the Niemeier lattices and their embeddings in the leech lattice Peer-reviewed

    M Harada, M Kitazume

    EUROPEAN JOURNAL OF COMBINATORICS　21　(4)　473-485　2000/05

    ISSN： 0195-6698

  155. Shadow lattices and shadow codes Peer-reviewed

    ST Dougherty, M Harada, P Sole

    DISCRETE MATHEMATICS　219　(1-3)　49-64　2000/05

    ISSN： 0012-365X

  156. Extremal self-dual codes with the smallest covering radius Peer-reviewed

    M Harada, M Ozeki

    DISCRETE MATHEMATICS　215　(1-3)　271-281　2000/03

    ISSN： 0012-365X

  157. Optimal formally self-dual codes over F-5 and F-7 Peer-reviewed

    ST Dougherty, TA Gulliver, M Harada

    APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING　10　(3)　227-236　2000/03

    DOI： 10.1007/s002000050126 　

    ISSN： 0938-1279

  158. Self-dual codes constructed from Hadamard matrices Peer-reviewed

    Masaaki Harada

    Math. J. Okayama Univ.　40 (1998)　15-21　2000

  159. On type II codes over F-4 Peer-reviewed

    K Betsumiya, TA Gulliver, M Harada, A Munemasa

    2000 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, PROCEEDINGS　47　141-141　2000

    DOI： 10.1109/18.945245 　

  160. Construction of optimal type IV self-dual codes over F-2+uF2 Peer-reviewed

    TA Gulliver, M Harada

    IEEE TRANSACTIONS ON INFORMATION THEORY　45　(7)　2520-2521　1999/11

    DOI： 10.1109/18.796394 　

    ISSN： 0018-9448

  161. Type IV self-dual codes over rings Peer-reviewed

    ST Dougherty, P Gaborit, M Harada, A Munemasa, P Sole

    IEEE TRANSACTIONS ON INFORMATION THEORY　45　(7)　2345-2360　1999/11

    DOI： 10.1109/18.796375 　

    ISSN： 0018-9448

  162. An optimal unimodular lattice in dimension 39 Peer-reviewed

    TA Gulliver

    JOURNAL OF COMBINATORIAL THEORY SERIES A　88　(1)　158-161　1999/10

    ISSN： 0097-3165

  163. On the covering radius of Z(4)-codes and their lattices Peer-reviewed

    T Aoki, P Gaborit, M Harada, M Ozeki, P Sole

    IEEE TRANSACTIONS ON INFORMATION THEORY　45　(6)　2162-2168　1999/09

    DOI： 10.1109/18.782168 　

    ISSN： 0018-9448

  164. New extremal self-dual codes of length 68 Peer-reviewed

    ST Dougherty, M Harada

    IEEE TRANSACTIONS ON INFORMATION THEORY　45　(6)　2133-2136　1999/09

    DOI： 10.1109/18.782158 　

    ISSN： 0018-9448

  165. Niemeier lattices and Type II codes over Z(4) Peer-reviewed

    A Bonnecaze, P Gaborit, M Harada, M Kitazume, P Sole

    DISCRETE MATHEMATICS　205　(1-3)　1-21　1999/07

    ISSN： 0012-365X

  166. Construction of an extremal self-dual code of length 62 Peer-reviewed

    M Harada

    IEEE TRANSACTIONS ON INFORMATION THEORY　45　(4)　1232-1233　1999/05

    DOI： 10.1109/18.761274 　

    ISSN： 0018-9448

  167. Type II codes, even unimodular lattices, and invariant rings Peer-reviewed

    E Bannai, ST Dougherty, M Harada, M Oura

    IEEE TRANSACTIONS ON INFORMATION THEORY　45　(4)　1194-1205　1999/05

    DOI： 10.1109/18.761269 　

    ISSN： 0018-9448

  168. Construction of extremal Type II codes over Z(4) Peer-reviewed

    P Gaborit, M Harada

    DESIGNS CODES AND CRYPTOGRAPHY　16　(3)　257-269　1999/05

    ISSN： 0925-1022

  169. Type II self-dual codes over finite rings and even unimodular lattices Peer-reviewed

    ST Dougherty, TA Gulliver, M Harada

    JOURNAL OF ALGEBRAIC COMBINATORICS　9　(3)　233-250　1999/05

    ISSN： 0925-9899

  170. Codes of lengths 120 and 136 meeting the Grey-Rankin bound and quasi-symmetric designs Peer-reviewed

    TA Gulliver, M Harada

    IEEE TRANSACTIONS ON INFORMATION THEORY　45　(2)　703-706　1999/03

    DOI： 10.1109/18.749017 　

    ISSN： 0018-9448

  171. Optimal ternary formally self-dual codes Peer-reviewed

    ST Dougherty, TA Gulliver, M Harada

    DISCRETE MATHEMATICS　196　(1-3)　117-135　1999/02

    ISSN： 0012-365X

  172. Extremal double circulant Type II codes over Z(4) and construction of 5-(24,10,36) designs Peer-reviewed

    TA Gulliver, M Harada

    DISCRETE MATHEMATICS　194　(1-3)　129-137　1999/01

    ISSN： 0012-365X

  173. On the Hamming weight enumerators of self-dual codes over Z(k) Peer-reviewed

    M Harada, M Oura

    FINITE FIELDS AND THEIR APPLICATIONS　5　(1)　26-34　1999/01

    ISSN： 1071-5797

  174. Type II codes over F-2+uF(2) Peer-reviewed

    ST Dougherty, P Gaborit, M Harada, P Sole

    IEEE TRANSACTIONS ON INFORMATION THEORY　45　(1)　32-45　1999/01

    DOI： 10.1109/18.746770 　

    ISSN： 0018-9448

  175. Self-dual codes over rings and the Chinese remainder theorem Peer-reviewed

    Steven T. Dougherty, Masaaki Harada, Patrick Solé

    Hokkaido Mathematical Journal　28　(2)　253-283　1999

    DOI： 10.14492/hokmj/1351001213 　

    ISSN： 0385-4035

  176. New optimal self-dual codes over GF(7) Peer-reviewed

    TA Gulliver, M Harada

    GRAPHS AND COMBINATORICS　15　(2)　175-186　1999

    DOI： 10.1007/s003730050038 　

    ISSN： 0911-0119

  177. Self-dual codes over Z(4) and unimodular lattices: A survey Peer-reviewed

    M Harada, P Sole, P Gaborit

    ALGEBRAS AND COMBINATORICS　255-275　1999

  178. Shadow optimal self-dual codes Peer-reviewed

    Steven T. Dougherty, Masaaki Harada

    Kyushu Journal of Mathematics　53　(2)　223-237　1999

    DOI： 10.2206/kyushujm.53.223 　

    ISSN： 1340-6116

  179. On binary extremal formally self-dual even codes Peer-reviewed

    Koichi Betsumiya, T. Aaron Gulliver, Masaaki Harada

    Kyushu Journal of Mathematics　53　(2)　421-430　1999

    DOI： 10.2206/kyushujm.53.421 　

    ISSN： 1340-6116

  180. Binary optimal linear rate 1/2 codes Peer-reviewed

    K Betsumiya, TA Gulliver, M Harada

    APPLIED ALGEBRA, ALGEBRAIC ALGORITHMS AND ERROR-CORRECTING CODES, PROCEEDINGS　1719　462-471　1999

    DOI： 10.1007/3-540-46796-3_44 　

    ISSN： 0302-9743

  181. New extremal self-dual codes of lengths 36 and 38 Peer-reviewed

    Masaaki Harada

    IEEE Transactions on Information Theory　45　(7)　2541-2543　1999

    Publisher: IEEE

    DOI： 10.1109/18.796402 　

    ISSN： 0018-9448

  182. Classification of extremal double-circulant self-dual codes of length up to 62 Peer-reviewed

    M Harada, TA Gulliver, H Kaneta

    DISCRETE MATHEMATICS　188　(1-3)　127-136　1998/06

    ISSN： 0012-365X

  183. Classification of Extremal Double Circulant Self-Dual Codes of Lengths 64 to 72 Peer-reviewed

    T. Aaron Gulliver, Masaaki Harada

    Designs, Codes, and Cryptography　13　(3)　257-269　1998

    Publisher: Springer Netherlands

    DOI： 10.1023/A:1008249924142 　

    ISSN： 0925-1022

  184. New Extremal Type II Codes over ℤ4 Peer-reviewed

    Masaaki Harada

    Designs, Codes, and Cryptography　13　(3)　271-284　1998

    Publisher: Springer Netherlands

    DOI： 10.1023/A:1008254008212 　

    ISSN： 0925-1022

  185. The existence of a formally self-dual even [70, 35, 14] code Peer-reviewed

    TA Gulliver, M Harada

    APPLIED MATHEMATICS LETTERS　11　(1)　95-98　1998/01

    DOI： 10.1016/S0893-9659(97)00140-7 　

    ISSN： 0893-9659

  186. New 5-designs constructed from the lifted Golay code over Z(4) Peer-reviewed

    M Harada

    JOURNAL OF COMBINATORIAL DESIGNS　6　(3)　225-229　1998

    ISSN： 1063-8539

  187. New extremal ternary self-dual codes Peer-reviewed

    Masaaki Harada

    Australasian J. Combin.　17　133-145　1998

  188. Double circulant self-dual codes over z(2k) Peer-reviewed

    TA Gulliver, M Harada

    1998 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY - PROCEEDINGS　44　151-151　1998

    DOI： 10.1109/18.737540 　

  189. Weighing matrices and self-dual codes Peer-reviewed

    M Harada

    ARS COMBINATORIA　47　65-73　1997/12

    ISSN： 0381-7032

  190. Extremal binary self-dual codes Peer-reviewed

    ST Dougherty, TA Gulliver, M Harada

    IEEE TRANSACTIONS ON INFORMATION THEORY　43　(6)　2036-2047　1997/11

    DOI： 10.1109/18.641574 　

    ISSN： 0018-9448

  191. The existence of a self-dual [70, 35, 12] code and formally self-dual codes Peer-reviewed

    Masaaki Harada

    Finite Fields and their Applications　3　(2)　131-139　1997/04

    DOI： 10.1006/ffta.1996.0174 　

    ISSN： 1071-5797

  192. Type II self-dual codes over finite rings and even unimodular lattices

    Steven T. Dougherty, T. Aaron Gulliver, Masaaki Harada

    IEEE International Symposium on Information Theory - Proceedings　207　1997

    DOI： 10.1109/ISIT.1997.613122 　

    ISSN： 2157-8095

  193. Classification of Extremal Double Circulant Formally Self-Dual even Codes Peer-reviewed

    T. Aaron Gulliver, Masaaki Harada

    Designs, Codes, and Cryptography　11　(1)　25-35　1997

    Publisher: Springer Netherlands

    DOI： 10.1023/A:1008206223659 　

    ISSN： 0925-1022

  194. Weight Enumerators of Double Circulant Codes and New Extremal Self-Dual Codes Peer-reviewed

    T. Aaron Gulliver, Masaaki Harada

    Designs, Codes, and Cryptography　11　(2)　141-150　1997

    Publisher: Springer Netherlands

    DOI： 10.1023/A:1008276604233 　

    ISSN： 0925-1022

  195. Certain self-dual codes over Z(4) and the odd Leech lattice Peer-reviewed

    TA Gulliver, M Harada

    APPLIED ALGEBRA, ALGEBRAIC ALGORITHMS AND ERROR-CORRECTING CODES　1255　130-137　1997

    DOI： 10.1007/3-540-63163-1_10 　

    ISSN： 0302-9743

  196. Weight enumerators of extremal singly-even [60, 30, 12] codes Peer-reviewed

    TA Gulliver, M Harada

    IEEE TRANSACTIONS ON INFORMATION THEORY　42　(2)　658-659　1996/03

    DOI： 10.1109/18.485739 　

    ISSN： 0018-9448

  197. Existence of new extremal doubly-even codes and extremal singly-even codes Peer-reviewed

    Masaaki Harada

    Des. Codes and Cryptogr.　8　273-283　1996

  198. New extremal doubly-even [64, 32, 12] codes Peer-reviewed

    Masaaki Harada, Hiroshi Kimura

    Designs, Codes and Cryptography　6　(2)　91-96　1995/09

    Publisher: Kluwer Academic Publishers

    DOI： 10.1007/BF01398007 　

    ISSN： 0925-1022 1573-7586

  199. Singly-even self-dual codes and hadamard matrices Peer-reviewed

    M Harada, VD Tonchev

    APPLIED ALGEBRA, ALGEBRAIC ALGORITHMS AND ERROR-CORRECTING CODES　948　279-284　1995

    ISSN： 0302-9743

  200. On extremal self-dual codes Peer-reviewed

    Masaaki Harada, Hiroshi Kimura

    Math. J. Okayama Univ　37　1-14　1995

    Publisher: Department of Mathematics, Faculty of Science, Okayama University

    ISSN： 0030-1566

Show all ︎Show first 5

Presentations 9

  1. On the nonexistence of certain extremal doubly even self-dual codes

    HARADA Masaaki

    2016/08/21

  2. On a 5-design related to an extremal doubly even self-dual code of length 72

    Workshop on Hadamard Matrices and Combinatorial Designs　2014/10/31

  3. 情報通信を支える１つの数学～誤り訂正符号という組合せ構造～

    原田 昌晃

    第５５回情報科学談話会　2014/10/12

  4. 非線形２元符号と Z4 符号 〜Nordstrom-Robinson 符号を例に〜

    応用数学連携フォーラム　2014/02/20

  5. On the residue codes of self-dual Z4-codes with large minimum Lee weights

    金沢組合せ論セミナー　2014/02/07

  6. 組合せ構造としての符号理論

    大談話会　2013/11/12

  7. Self-dual code とその周辺（特別講演） Invited

    原田 昌晃

    日本数学会 2013 年度秋季総合分科会　2013/09/24

  8. Magma へ貢献できること

    原田 昌晃

    2012/07/22

  9. Self-dual codes -an introduction-（特別講演） Invited

    原田 昌晃

    代数学と計算　2011/11/08

Show all Show first 5

Research Projects 28

  1. Evolution of Combinatorial Coding Theory

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2023/04/01 - 2028/03/31

  2. 代数的符号理論の総合的研究

    原田 昌晃

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業 基盤研究(B)

    Category: 基盤研究(B)

    Institution: 東北大学

    2019/04 - 2024/03

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    代数的符号理論の重要な対象としてself-dual code があり、代数的および組合せ論的な研究が活発に行われている。 本研究課題では、研究代表者が今までに精力的に研究を行って来た self-dual code を研究対象の中心とし、組合せ論の研究における基本的なテーマでもある存在と分類について取り組んでいる。特に、整数論との関係も深いunimodular lattice やdesign などの組合せ構造との関連を重視するだけでなく、新たな研究対象への応用（関連）の確立を目指している。また、最近、暗号理論への応用が見つかったlinear complementary dual (LCD) code や代数的符号理論の範疇に留まらずに新たな応用や実用化が期待される量子符号などの研究にも取り組み、新たなる展開を目指して代数的符号理論の総合的な研究を行う。 self-dual code の分類と構成は、基本的なテーマではあるがcode 自身が非常に簡単な構造をしていることから他の分野での問題をcode の構成や分類に帰着させて解決させることが出来る可能性があり、他の分野との関連性で非常に威力を発揮する重要なテーマである。これまでの結果を基盤にして、新たな構成方法の構築を行うことで有限体だけでなく有限環上の code、特にextremal self-dual Zk-code の構成に挑戦した。 linear complementary dual (LCD) code はMassey によって1996 年に導入されたクラスであるが、2010 年にCarlet-Guilleyによって暗号理論への新たな応用が新たに見つかった。これまでに研究代表者および分担者を中心としてこれまでに行ってきたself-dual code の研究を基盤として、LCD code の構成および分類問題に取り組んだ。

  3. 代数的符号理論の総合的研究 Competitive

    原田 昌晃

    System: 基盤研究(B)

    2015/04 - 2019/03

  4. Graph representations of combinatorial structures

    Araya Makoto

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Shizuoka University

    2015/04/01 - 2018/03/31

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    By a graph representation of a linear code over finite ring, we give classifications of a certain class of self-complementary codes for modest lengths. As a consequence we give quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices. We classify ternary maximal self-orthogonal codes of lengths 21,22 and 23 by a graph representation. We classify partially balanced incomplete block designs by given association schemes and its automorphism groups. For bipartite graphs and association schemes, we classify some partially balanced incomplete block designs. Each graphs are a representation of designs.

  5. Various aspects of sporadic simple groups

    KITAZUME MASAAKI, SAWABE Masato, MUNEMASA Akihiro, CHIGIRA Naoki, HARADA Masaaki, ABE Toshiyuki, SHIMAKURA Hiroki, NAKASORA Hiroyuki, HORIGUCHI Naoyuki, IRIE Yuuki, KOBAYASHI Yusuke

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Chiba University

    2012/04/01 - 2018/03/31

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    We have studied the Rudvalis simple group and related algebraic structures (code, lattice) and combinatorial structure (graph, design). Consequently we show the existence of even self-dual code preserved by the Rudvalis group, and give a combinatorial description of some generator. We further define five 2-designs by using a unitary group, and give a new construction of the Rudvalis graph from these 2-designs. We also consider Conway's theorem, which show the relation between the Rudvalis graph and the Hoffman-Singleton graph. Moreover we have completed the classification of extremal doubly even self-dual codes with 2-transitive automorphism groups by showing non-existence of the remaining case.

  6. 組合せデザインと格子によるある自己双対符号の存在問題の解決への試み Competitive

    原田 昌晃

    System: 挑戦的萌芽研究

    2014/04 - 2016/03

  7. 代数的符号理論の新展開を目指して Competitive

    原田 昌晃

    System: 基盤研究(B)

    2011/04 - 2015/03

  8. 長さ７２の極値的重偶自己双対符号の構成への試み Competitive

    原田 昌晃

    System: 挑戦的萌芽研究

    2011/04 - 2013/03

  9. 代数的符号理論による組合せ構造の解析と量子符号への応用 Competitive

    原田 昌晃

    Offer Organization: 科学技術振興機構

    System: 戦略的創造研究推進事業・さきがけ

    2008/10 - 2012/03

  10. 代数的符号理論と組合せデザイン Competitive

    原田 昌晃

    System: 基盤研究(C)

    2008/04 - 2011/03

  11. Research on algebraic coding theory and its applications for vertex operator algebras

    BETSUMIYA Koichi, MUNEMASA Akihiro, HARADA Masaaki, YAMAUCHI Hiroshi, SHIMAKURA Hiroki, LAM Ching Hung

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Jobu University

    2007 - 2010

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    We have presented an efficient algorithm for finding triply even codes by investigating the structure of triply even codes. This algorithm has produced a classification of maximal triply even codes of length up to 48. As a result, we have found a new maximal triply even code which is contrary to the expected behavior constructed by a triangular graph. Moreover, new framed vertex operator algebras have been constructed from the list of codes.

  12. Study on algebraic or combinatorial structures whose automorphism groups contain finite simple groups

    KITAZUME Masaaki, NOZAWA Sohei, KOSHITANI Shigeo, SAWABE Masato, SUGIYAMA KenーIchi, ANDO Tetsuya, YAMADA Hiromichi, MUNEMASA Akihiro, HARADA Masaaki, CHIGIRA Naoki, ABE Thoshiyuki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Chiba University

    2007 - 2010

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    We have studied some algebraic structures and combinatorial structured whose automorphism groups contain finite simple groups. (1) We have studied the binary code spanned by the sets of fixed points of the involutions of a finite transitive permutation group and its dual code. New self-dual codes invariant under the Hall-Janko group and the Rudvalis group have been constructed, respectively. (2) We have studied rank 3 graphs related to some sporadic simple groups (especially, HJ, Suz, M24). New constructions of these rank 3 graphs from some designs have been obtained. (3) We have determined the minimum value m such that a given Niemeier lattice is a m-neighbor of the Leech lattice.

  13. 代数的符号理論と組合せデザイン Competitive

    原田 昌晃

    System: 若手研究(B)

    2005/04 - 2008/03

  14. Applications of algebraic methods in coding theory to combinatorial designs and discrete geometry

    MUNEMASA Akihiro, HARADA Masaaki, TANIGUCHI Tetsuji, IMAI Hideo, URAKAWA Hajime, ASOH Toru, TAYA Hisao, BETSUMIYA Koichi

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2005 - 2008

  15. Coding theory, the invariant theory for the finite fractional linear transformation groups and their applications to the number theory

    OZEKI Michio, BANNAI Eiichi, KIZUME Masaaki, SAWADA Hideki, MURABAYASHI Naoki, NISHIMURA Takuji

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Yamagata University

    2005 - 2006

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    Ozeki has obtained a remarkable result concerning the 40 dimensional even unimodular lattices. The result says that there are a pair of non equivalent 40 dimensional even unimodular lattices whose Siegel theta series of degree up to 2 coincide but Siegel theta series of degree 3 differ. Ozeki has recently completed the result as a research paper under the title "On a problem posed by S. Manni". Ozeki has conceived a new approach to the problem of determining the covering radius of n dimensional lattice covering by equal spheres, and he is preparing a research paper under the title "Two approaches to the lattice covering of whole space with equal spheres in general dimensions. He is now investigating the coset weight distributions of second order Reed-Muller code of length 64. Sawada has published two research papers including a paper entitled "On the utility of a bilateral system". Bannai has published seven research papers including a paper entitled "A note on integral Euclidean lattices in dimension 3". Kitazume has published two research papers which discuss the relation between the finite permutation groups and the self-dual codes. Murabayashi has published a paper entitled.

  16. Finite Simple Groups and Related Codes, Lattices and Vertex Operator Algebras

    KITAZUME Masaaki, KOSHITANI Shigeo, NOZAWA Sohei, SUGIYAMA Ken-ichi, HARADA Masaaki, CHIGIRA Naoki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Chiba University

    2003 - 2006

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    We have studied codes, lattices and vertex operator algebras related to finite simple groups. Main results are as follows : 1. We studied singly even codes of length 48 and odd unimodular lattices of rank 48 which have (resp. do not have) extremal neighbors. As a byproduct, we have constructed a new extremal code over Z/4Z. 2. We studied a putative extremal binary code of length 72. We showed that if there is a self-orthogonal 5-(72,16,78) design then the rows of its block-point incidence matrix generate an extremal doubly-even self-dual code of length 72. 3. We constructed new self-dual codes of length 100 invariant under the Hall-Janko group. We studied the binary code C(G, n) defined as the dual code of the code spanned by the sets of fixed points of involutions of a given group G. We showed that any G-invariant self-orthogonal code of length n is contained in C(G, n). Many self-orthogonal codes related to sporadic simple groups, including the extended Golay code and the above code for the Hall-Janko group, are obtained as C(G, n). Some new self-dual codes invariant under sporadic almost simple groups are constructed. 4. We constructed extremal singly even self-dual [64,32,12] codes with weight enumerators which were not known to be attainable. In particular, we find some codes whose shadows have minimum weight 12. By considering their doubly even neighbors, extremal doubly even self-dual [64,32,12] codes with covering radius 12 are constructed for the first time. 5. We studied maximum cocliques of sporadic rank 3 graphs and related designs. We gave some reconstructions of the Hall-Janko graph from the Witt system and the hexacode. Moreover we considered the maximum coclique design of the sporadic Suzuki graph. We constructed a new 3-(66,16,21) design with the automorphism group U_{3}(4):4, the unitary group over the 16-element field. By using this design, we gave a new construction of the sporadic Suzuki graph.

  17. 代数的符号理論と格子、組合せデザイン、および量子符号への応用 Competitive

    原田 昌晃

    System: 若手研究(B)

    2002/04 - 2005/03

  18. 基礎科学研究助成金 Competitive

    原田 昌晃

    Offer Organization: (財)住友財団

    System: 基礎科学研究助成金

    2005 -

  19. 誤り訂正量子符号の有限群論的アプローチ

    北詰 正顕, 杉山 健一, 桜井 貴文, 野澤 宗平, 宗政 昭弘, 原田 昌晃, 大坪 紀之

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 萌芽研究

    Institution: 千葉大学

    2002 - 2004

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    (1)本年度においては,まず,Calderbank-Rains-Shor-Sloaneの仕事との関連から重要であると思われるGF(4)上の(特に線形でない)符号の構成について考えた。分担者の宗政・原田とは,前年度までの方針に則り48次元のunimodular latticeから得られる長さ24の非線形符号の構成を試みたが,条件の良いlatticeを見つけることができず成果を得るには至らなかった。この研究の過程から副産物として得られた48次元の符号と格子に関する結果は論文として公表した。そこでは,特に,剰余整数環Z/4Z上の新しい(良い)符号を発見している。このような剰余整数環上の符号と,4元体上の符号,あるいは,量子符号,との関連も模索したが,はっきりしなかった。 (2)分担者の杉山とは,代数幾何符号の観点からのアプローチを検討した。その結果,柴木氏(岩手県立宮古短期大学)の協力を得て,特異点を持つ代数曲線から、線形符号を作る方法を得た。この方法は構成が簡単で、さらに復号化もしやすいという利点をもつ。これについては,論文として準備中である。この方法は色々な体に適用できるため,GF(4)の場合について検討を加えたが,現時点では良い符号を得ることは出来なかった。 (3)最後に,本研究の「有限群論的アプローチ」という精神を生かすべく,符号に(大きな)有限群が作用するという条件を積極的に使うような理論を考えてみた。その結果,千吉良直紀氏(室蘭工業大学)の研究協力を得て,GF(2)上の(すなわち古典的)符号についてはある種の上限を与える定理を得て,学会発表を行い,論文として準備している。これを他の体(特にGF(4))について拡張することは,今後の課題であると考える。

  20. A study of the interacting area among the theory of quadratic forms and the theory of modular forms and the algebraic coding theory

    OZEKI Michio, KITAZUME Masaaki, MUNEMASA Akihiro, HARADA Masaaki, SAWADA Hideki, MURABAYASHI Naoki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Yamagata University

    2002 - 2004

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    The present research has been done in the period between year 2002 and 2004 under the GRANT-IN-AID sponcered by the Ministry of Education, Culture, Sports, Science and Technology. In the application the head investigator raised five reseach purposes : (1)a study of the ineraction between the coding theory and the theory of modular forms, (2)a study of the lattices constructed from the binary self-dual code and the tertiary self dual codes, (3)the covering radius problem for the n-dimensional lattices, (4)the covering radius problem for non self-dual linear codes, (5)an interaction bewtween the coding theory and the cryptology. As to the purpose (1) we get some results and gave 4 talks and are preparing the research papers. As to (2) we have published one research paper and are preparing one paper. As to (3) the result is not mature for writing a paper. As to (4) we gave two talks and are preparing some research papers. There is no actual activity fot the purpose (5). Besides the research purpose we have published three research papers.

  21. Comprehensive study on Algebraic Combinatorics

    BANNAI Eiichi, MUNEMASA Akihiro, BANNAI Etsuko, ITO Tatsuro, SUZUKI Hiroshi, KOIKE Masao

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Kyushu University

    2001 - 2003

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    One of the goal of this grant is to widely contribute to the advancement of algebraic combinatorics in Japan through workshops and travel aid. During the fiscal year 2001-2003, the grant was used to partly support : The 18th, 19th, 20th Algebraic Combinatoric Symposiums (at resp. Chiba University, Kumamoto University, Hokkaio University), three symposiums entitled "Algebraic Combinatorics" at RIMS, three workshops on areas related to automorphic forms at Hamamatsu (Ibukiyama, Bannai, Saito, Miyamoyo organizers). Symposium at Yamagata (Nov. 2002), International Conference EA- CAC2 held in Fukuoka (Bannai organizer, Nov. 2003). Research in Algebraic Combinatorics in Japan is showing steady progress. The progress covers diverse areas such as distant-regular graphs, association schemes, codes, designs, lattices, modular forms. The results of the principal invstigator includes: (i) Character tables of commutative association schemes and Ramanujan graphs, (ii) Relations between codes, lattices and modular forms, (iii) Tight 4-, 5-, 7-designs on spheres (Bannai Munemasa-Venkov), (iv) Tight designs/codes over Grassmanian spaces (Bachoo-Bannal Coulangeon). In addition, the pricinpal investigator studied designs on Euclidean spaces: Collaborating with Etsuko Bannai, the classification of tight 4-designs with constant weight, the classification of Gaussian tight 4-designs, and the classification of optimal tight 4-designs on two concentric spheres were completed. We are currently challenging more general classi-fications. Jointly with Makoto Tanabe, we participated in the verification of Oleg Musin's spectacular result: The determination of the Kissing number in dimension four, and helped the completion of Musin's proof.

  22. ALGEBRAIC CODING THEORY, COMBINATORIAL DESIGNS AND ASSOCIATION SCHEMES

    MUNEMASA Akihiro, URAKAWA Hajime, BANNAI Etsuko, BANNAI Eiichi, HIRAKI Akira, HARADA Masaaki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    2000 - 2003

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    A generalization of the concept of a type II code has been obtained for arbitrary finite fields of characteristic two, and the mass formulas for such codes have been obtained. This allowed us to classify nearly all type II codes whose binary lengths are at most 32, and our results were presented in the 14th AAECC symposium in Australia. We have solved a long standing problem of the existence of tight spherical designs, and this result was presented in an international conference on combinatorics in the Netherlands in 2002.Our result uses the theory of modular forms, and we participated in an international conference on modular forms in 2004 in order to find more connections between combinatorics and the theory of modular forms. We also explored the connections between integral lattices with binary codes, and spherical designs with ordinary combinatorial designs. We have established a uniqueness of a certain self-orthogonal 5-design related to a binary self-dual code, and we have submitted a paper about this result.

  23. 有限環上の代数的符号理論と格子および組合せデザインとの関係についての研究 Competitive

    原田 昌晃

    System: 奨励研究(A)

    2000/04 - 2002/03

  24. Finite Simple Groups and Related Codes, Lattices and Vertex Operator Algebras

    KITAZUME Masaaki, SUGIYAMA Ken-ichi, NOZAWA Sohei, KOSHITANI Shigeo, HARADA Masaaki, YAMADA Niromichi

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Chiba University

    2000 - 2002

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    We have studied codes, lattices and vertex operator algebras related to finite simple groups. Main results are as follows : 1.The classifications of the 2-and 3-radical subgroups of Fischer's simple groups F_<22>, F_<23>, F'_<24> have been completed. 2.Even unimodular Gaussian lattices of dimension 12 have been classified. 3.A sufficient condition for extremal Z_6-codes, and as an application, many Z_6-code related the Leech lattice had been constructed. Moreover the self-dual Z_6-codes of length 8 are classified. 4.The construction method of unimodular lattices using ternary self-dual codes has been studied. Extremal odd unimodular lattices in dimensions 44, 60 and 68 are constructed for the first time. 5.The constructions of vertex operator algebras using Z_8-codes and subalgebras V_<√<2>A_3> have been considered. We also give a complete decomposition of the Moonshine VOA V^* associated with some subalgebra given by an embedding of the lattice (√<2>A_3)^8 into the Leech lattice. 6.By using Z_3-orbifold construction given by Dong-Mason, we give a complete decomposition of the Moonshine VOA V^* associated with some subalgebra given by an embedding of the lattice (√<2>A_2)^<12> the Leech lattice. We also give the explicit actions of certain 3A-elements of the Monster simple group on V^* are defined.

  25. 代数的符号理論とユニモジュラ格子の研究 Competitive

    原田 昌晃

    System: 奨励研究(A)

    1998/04 - 2000/03

  26. 暗号系に現れる群構造について

    澤田 秀樹, 原田 昌晃, 村林 直樹

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 萌芽的研究

    Institution: 山形大学

    1998 - 2000

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    昨年度はブロック暗号の鍵の持つ群論的特徴について考察し,ブロック暗号の鍵の集合の候補と考えられる,有限群Gの部分集合Uで条件 (i)集合UUと集合Uとの共通部分が空集合,または (ii)集合UUUと集合Uとの共通部分が空集合 を満足するものの構成法の一つを群論的に示した。すなわち 1.Gの適当な部分群Hを構成する。 2.HのGにおける正規化群Nを構成する。 3.剰余群N/Hにおいて位数が3以上の元nH(n∈N)を見つけ,その剰余類nHをUとおく。 であった。引き続き今年度は上の計算を実行するアルゴリズムを具体的に提案し,代数学ソフトGAPによる計算を行った。またその過程においてどのようなブロック暗号にも理論的にはMeet-in-the-middle attackと言う群論的な攻撃が可能であることを証明し,やはりGAPを使用した攻撃例も示した。この結果は電子情報通信学会英文論文誌Aの離散数学とその応用特集号に掲載の予定である。 さらにこの研究の遂行に必要なGAPやC言語のプログラミングに関する専門書も出版することができた。

  27. Algebraic Coding Theory and the related studies of algebraic, geometric and analytic natures

    OZEKI Michio, SANO Takashi, MURABAYASHI Naoki, UCHIDA Fuichi, HARADA Masaaki, UENO Keisuke

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B).

    Institution: Faculty of Science, Yamagata University

    1997 - 2000

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    Ozeki, the research project organizer, and the other researchers have developped the methods to study some basic problems in the theory of error-correcting code such as the determination of the covering radii of codes, the existence question of extremal self-dual codes, the coset weight distributions of codes, the shadow theory of codes, the mass formulas for the classes of codes, the classification problem of codes. And he and the co-workers attained many remarkable results. More concretely, he has succeeded in the followings : (i) giving the results on extremal singly even self-dual binary [40, 20, 8] codes, among which a code with the covering radius of 7 is included, and this results have been published by Discrete Mathematics, (ii) developing a decisive method to treat the covering radius problem and the determination of the complete coset weight distributions of doubly even self-dual binary codes, and by using this method he has determined the complete coset weight distributions and the covering radius of extremal doubly even self-dual binary [40, 20, 8] codes, this results has been published by Theoretical Computer Science. Vol. 235, (iii) sharpening the method in (ii) to the large extent and he has determined the covering radius of extremal doubly even self-dual binary [56, 28, 12] codes, and this result has been published by IEEE transaction on Information Theory, The co-researcher F.Uchida has studied the differentiable action of the non-compact Lie group Sp (p, q) on the 4p + 4q - 1 dimensional sphere. The co-researcher N.Murabayashi has studied concerning the zeta functions of the abelian surfaces of CM type, and he has obtained some results on them. The co-researcher T.Sano has studied the construction of the Kac algebras, and the commutavity problem of the automorphisms of the standard type, and he is preparing the research papers. The co-researcher K.Ueno studies the problem of the boundaries at infinity of the harmonic maps between the Carnot spaces. The co-researcher M.Harada studies self-dual codes over finite rings, and the relations of the codes with other subareas of disctrete mathematics, espacially the relations between the unimodular lattices and the combinatorial designs.

  28. 有限環上の代数的符号理論と組合せデザインおよびラティスの関係 Competitive

    原田 昌晃

    Offer Organization: (財)住友財団

    System: 基礎科学研究助成金

    1999 -

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