• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

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

Research Project

Project/Area Number 17340020
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionTohoku University

Principal Investigator

MUNEMASA Akihiro  Tohoku University, 大学院・情報科学研究科, 教授 (50219862)

Co-Investigator(Kenkyū-buntansha) HARADA Masaaki  山形大学, 理学部, 准教授 (90292408)
今井 秀雄  東北大学, 大学院・情報科学研究科, 准教授 (10093668)
田谷 久雄  宮城教育大学, 教育学部, 准教授 (40257241)
別宮 耕一  上武大学, ビジネス情報学部, 准教授 (60364684)
浦川 肇  東北大学, 大学院・情報科学研究科, 教授 (50022679)
Co-Investigator(Renkei-kenkyūsha) TANIGUCHI Tetsuji  松江工業高等専門学校, 数理科学科, 助教 (90543728)
IMAI Hideo  東北大学, 大学院・情報科学研究科, 准教授 (10093668)
URAKAWA Hajime  東北大学, 大学院・情報科学研究科, 教授 (50022679)
ASOH Toru  東北大学, 大学院・情報科学研究科, 准教授 (00111352)
TAYA Hisao  宮城教育大学, 教育学部, 准教授 (40257241)
BETSUMIYA Koichi  弘前大学, 理工学部, 准教授 (60364684)
Project Period (FY) 2005 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥6,970,000 (Direct Cost: ¥6,100,000、Indirect Cost: ¥870,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2007: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2006: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2005: ¥1,400,000 (Direct Cost: ¥1,400,000)
Keywords応用数学 / 代数的組合せ論 / 符号理論 / 離散幾何 / 組合せデザイン理論 / 置換群論 / グラフ理論 / 代数的符号理論 / 自己双対符号 / 有限体 / 格子 / 組合せデザイン / 国際情報交換 / ブルガリア : オランダ
Research Abstract

自己双対符号の性質を考察したこと、およびその中で特異なものを分類したことが主な成果である。特に、整数格子の分類結果を応用することにより、これまで分類することができなかった3元や5元自己双対符号についても分類方法を確立した。また、関連した組合せ論の研究として、有限体からできる強正則グラフとアソシエーションスキームの構成、組合せデザインの構成にも取り組んだ。

Report

(5 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (39 results)

All 2009 2008 2007 2006 2005 Other

All Journal Article (24 results) (of which Peer Reviewed: 14 results) Presentation (13 results) Remarks (2 results)

  • [Journal Article] Classification of ternary extremal self-dual codes of length 282009

    • Author(s)
      M. Harada, A. Munemasa, B. Venkov
    • Journal Title

      Math.Comp. 78

      Pages: 1787-1796

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] There exists no self-dual[24,12,10]code over F5, Designs2009

    • Author(s)
      M. Harada, A. Munemasa
    • Journal Title

      Codes and Cryptography 12

      Pages: 125-127

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] There exists no self-dual [24, 12, 10] code over F52009

    • Author(s)
      M. Harada, A. Munemasa
    • Journal Title

      Designs, Codes and Cryptography 12

      Pages: 125-127

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On graphs with the smallest eigenvalue at least-1-square root 22008

    • Author(s)
      T. Taniguchi
    • Journal Title

      Ars Math. Contemp 1

      Pages: 81-98

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Determination of weight enumerators of binary extremal self-dual[42,21,8]codes2008

    • Author(s)
      S. Bouyuklieva, M. Harada, A. Munemasa
    • Journal Title

      Finite Fields and Their Applications 14

      Pages: 177-187

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A new example of non-amorphous association schemes2008

    • Author(s)
      T. Ikuta, A. Munemasa
    • Journal Title

      Contributions to Discrete Mathematics 3

      Pages: 31-36

    • Related Report
      2008 Annual Research Report 2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Determination of weight enumerators of binary extremal self?dual [42, 21, 8] codes2008

    • Author(s)
      S. Bouyuklieva, M. Harad a, A. Munemasa
    • Journal Title

      Finite Fields and Their Applications 14

      Pages: 177-187

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the covering radii of extremal doubly even self-dual codes2007

    • Author(s)
      M. Harada, A. Munemasa
    • Journal Title

      Adv.Math.Commun 1

      Pages: 251-256

    • NAID

      120003728106

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Simple abelian quadruple systems2007

    • Author(s)
      A. Muneamsa, and M. Sawa
    • Journal Title

      J.Combin.Theory, Ser A 114

      Pages: 1160-1164

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the covering radii of extremal doubly even self-dual codes2007

    • Author(s)
      M. Harada and A. Munemasa
    • Journal Title

      Adv. Math. Commun. 1

      Pages: 251-256

    • NAID

      120003728106

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Simple abelian quadruple systems2007

    • Author(s)
      A. Munemasa and M. Sawa
    • Journal Title

      J. Combin. Theory, Ser. A 114 114

      Pages: 1160-1164

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some restrictions on weight enumerators of singly even self-dual codes2006

    • Author(s)
      M. Harada, A. Munemasa
    • Journal Title

      IEEE Trans. Inform. Theory 52

      Pages: 1266-1269

    • NAID

      120002337725

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hyperplane partitions and difference systems of sets2006

    • Author(s)
      R. Fuji-Hara, A. Munemasa, V. D. Tonchev
    • Journal Title

      J.Combin.Theory, Ser. A, 113

      Pages: 1689-1698

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Some restrictions on weight enumerators of singly even self-dual codes2006

    • Author(s)
      M.Harada, A.Munemasa
    • Journal Title

      IEEE Trans. Inform. Theory 52

      Pages: 1266-1269

    • NAID

      120002337725

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Hyperplane partitions and difference systems of sets2006

    • Author(s)
      R.Fuji-Hara, A.Munemasa, V.Tonchev
    • Journal Title

      J. Combinatorial Theory, Ser. A 113

      Pages: 1689-1698

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Orthogonal designs and MDS self-dual codes2006

    • Author(s)
      M.Harada, H.Kharaghani
    • Journal Title

      Australasian Journal of Combinatorics 35

      Pages: 57-67

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Classification of extremal double circulant self-dual codes of lengths 74-882006

    • Author(s)
      T.A.Gulliver, M.Harada
    • Journal Title

      Discrete Mathematics 306

      Pages: 2064-2072

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Binary singly even self-dual codeに関連したextremal problem2006

    • Author(s)
      A.Munemasa
    • Journal Title

      京都大学数理解析研究所講究録 1465

      Pages: 130-137

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Self-orthogonal 3-(56,12,65) designs and extremal doubly-even self-dual codes of length 562006

    • Author(s)
      M.Harada
    • Journal Title

      Designs, Codes and Cryptography 38

      Pages: 5-16

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On some self-dual codes and unimodular lattices in dimension 482005

    • Author(s)
      M.Harada, M.Kitazume, A.Munemasa, B.Venkov
    • Journal Title

      European Journal of Combinatorics 26

      Pages: 543-557

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A characterization of designs related to an extremal doubly-even self-dual code of length 482005

    • Author(s)
      M.Harada, A.Munemasa, V.D.Tonchev
    • Journal Title

      Annals of Combinatorics 9

      Pages: 189-198

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Remark on a 5-design related to a putative extremal doubly-even self-dual [96,48,20] code2005

    • Author(s)
      M.Harada
    • Journal Title

      Designs, Codes and Cryptography 37

      Pages: 355-358

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Ozeki polynomials and Jacobi forms2005

    • Author(s)
      K.Betsumiya, Y.Choie
    • Journal Title

      Ars Combinatoria 77

      Pages: 233-244

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Mass formula for self-orthogonal codesover Z_p^2, Journal of Combinatorics

    • Author(s)
      R. A. L. Betty, A. Munemasa
    • Journal Title

      Information & System Sciences (掲載受理)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Presentation] On graphs whose smallest eigenvalue is at least-32008

    • Author(s)
      谷口哲至
    • Organizer
      Geometric and Algebraic Combinatorics 4
    • Place of Presentation
      Oisterwijk, オランダ王国
    • Year and Date
      2008-08-21
    • Related Report
      2008 Final Research Report
  • [Presentation] On some cyclotomic association schemes and strongly regular graphs2008

    • Author(s)
      宗政昭弘
    • Organizer
      Geometric and Algebraic Combinatorics 4
    • Place of Presentation
      Oisterwijk, オランダ王国
    • Year and Date
      2008-08-18
    • Related Report
      2008 Final Research Report
  • [Presentation] On some cyclotomic association schemes and strongly regular graphs2008

    • Author(s)
      宗政昭弘
    • Organizer
      Geometric and Algebraic Combinatorics 4
    • Place of Presentation
      Oisterwijk, the Netherl ands
    • Year and Date
      2008-08-18
    • Related Report
      2008 Annual Research Report
  • [Presentation] 長さ28のエクストリーマル3元自己双対符号の分類2007

    • Author(s)
      宗政昭弘
    • Organizer
      代数学と計算
    • Place of Presentation
      首都大学東京
    • Year and Date
      2007-12-05
    • Related Report
      2008 Final Research Report
  • [Presentation] 長さ28の極値的3元自己双対符号の分類2007

    • Author(s)
      宗政昭弘
    • Organizer
      第7回代数学と計算研究集会
    • Place of Presentation
      首都大学東京
    • Year and Date
      2007-12-05
    • Related Report
      2007 Annual Research Report
  • [Presentation] Mass formula for codes2007

    • Author(s)
      宗政昭弘
    • Organizer
      第19回有限群論草津セミナー
    • Place of Presentation
      草津セミナーハウス
    • Year and Date
      2007-08-03
    • Related Report
      2007 Annual Research Report
  • [Presentation] On graphs with the smalleset eigenvelue at least-1-square root 22007

    • Author(s)
      谷口哲至
    • Organizer
      Sixth Slovenian International Conference on Graph Theory
    • Place of Presentation
      Bled, スロベニア
    • Year and Date
      2007-06-26
    • Related Report
      2008 Final Research Report
  • [Presentation] On Graphs with Complete Multipartite mu-Graphs2007

    • Author(s)
      宗政昭弘
    • Organizer
      Sixth Slovenian International Conference on Graph Theory
    • Place of Presentation
      Bled, スロベニア
    • Year and Date
      2007-06-25
    • Related Report
      2008 Final Research Report
  • [Presentation] On graphs with complete multipartite mu-graphs2007

    • Author(s)
      宗政昭弘
    • Organizer
      The 6th Slovenian International Conference on Graph Theory
    • Place of Presentation
      Lake Bled(Slovenia)
    • Year and Date
      2007-06-25
    • Related Report
      2007 Annual Research Report
  • [Presentation] On Graphs with Complete Multipartite mu-Graphs2007

    • Author(s)
      宗政昭弘
    • Organizer
      Korea-Japan Workshop on Algebra and Combinatorics
    • Place of Presentation
      釜山国立大学, 韓国
    • Year and Date
      2007-02-10
    • Related Report
      2008 Final Research Report
  • [Presentation] Combinatorial structures derived from extremal even unimodular lattices2006

    • Author(s)
      宗政昭弘
    • Organizer
      Algebra and Combinatorics
    • Place of Presentation
      Ateneo de Manila University, フィリピン共和国
    • Year and Date
      2006-04-01
    • Related Report
      2008 Final Research Report
  • [Presentation] Covering radii of extremal binary doubly even self-dual codes The Asian Symposium on Computer Mathematics 20052005

    • Author(s)
      宗政昭弘
    • Organizer
      Korean Institute of Advanced Study
    • Place of Presentation
      韓国
    • Year and Date
      2005-12-10
    • Related Report
      2008 Final Research Report
  • [Presentation] 組合せデザインとその周辺における数理的基礎およびそれらの応用2005

    • Author(s)
      宗政昭弘
    • Organizer
      An extremal problem related to binary singly even self-dual codes
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2005-08-04
    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

      http://www.math.is.tohoku.ac.jp/~munemasa/selfdualcodes.htm

    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

      http://www.math.is.tohoku.ac.jp/~munemasa/selfdualcodes.htm

    • Related Report
      2008 Annual Research Report

URL: 

Published: 2005-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi