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

Research Project

Project/Area Number 19540048
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionJobu University

Principal Investigator

BETSUMIYA Koichi  Jobu University, 大学院・理工学研究科, 准教授 (60364684)

Co-Investigator(Kenkyū-buntansha) MUNEMASA Akihiro  東北大学, 大学院・情報科学研究科, 教授 (50219862)
HARADA Masaaki  山形大学, 理学部, 准教授 (90292408)
YAMAUCHI Hiroshi  東京女子大学, 講師 (40452213)
Research Collaborator SHIMAKURA Hiroki  愛知教育大学, 教育学部, 講師 (90399791)
LAM Ching Hung  台湾中央研究所, 教授
Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords群論 / 符号理論
Research Abstract

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.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (35 results)

All 2011 2010 2009 2008 2007 Other

All Journal Article (15 results) (of which Peer Reviewed: 15 results) Presentation (13 results) Remarks (7 results)

  • [Journal Article] Hadamard matrices of order 32 and extremal ternary self-dual codes2011

    • Author(s)
      別宮耕一・原田昌晃・木村浩
    • Journal Title

      Designs, Codes and Cryptography 58

      Pages: 203-214

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hadamard matrices of order 32 and extremal ternary self-dual codes2011

    • Author(s)
      Koichi Betsumiya, Masaaki Harada, Hiroshi Kimura
    • Journal Title

      Designs, Codes and Cryptography

      Volume: 59 Pages: 203-214

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The FLM conjecture and framed VOA、Vertex operator algebras and related areas2009

    • Author(s)
      Lam, Ching Hung・山内博
    • Journal Title

      Contemporary Mathematics 497

      Pages: 125-138

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Mass formula for even codes over Z_8、Cryptography and Coding2009

    • Author(s)
      別宮耕一・Rowana Alma L.Betty・宗政昭弘
    • Journal Title

      Springer LNCS 5921

      Pages: 65-77

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Mass formula for even codes over Z_82009

    • Author(s)
      別宮耕一・Rowana Alma L. Betty・宗政昭弘
    • Journal Title

      Cryptography and Coding, Springer LNCS 5921

      Pages: 65-77

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Invariant Ring of Clifford-Weil Group, and Jacobi Forms over Totally Real Field2009

    • Author(s)
      Koichi Betsumiya, YoungJu Choie
    • Journal Title

      Seminaires et Congres 21

      Pages: 1-16

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Mass Formula for Even Codes over Z_82009

    • Author(s)
      Koichi Betsumiya, Rowena Alma L.Betty, Akihiro Munemasa
    • Journal Title

      Cryptography and Coding, Springer LNCS 5921

      Pages: 65-77

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Minimum Lee weights of Type II code over F_2^r2008

    • Author(s)
      別宮耕一
    • Journal Title

      Discrete Mathematics 308

      Pages: 3018-3022

    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On the structure of framed vertex operator algebras and their pointwise frame stabilizers2008

    • Author(s)
      C.H.Lam・山内博
    • Journal Title

      Communications in Mathematical Physics 277

      Pages: 237-285

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the structure of framed vertex operator algebras and their pointwise frame stabilizers2008

    • Author(s)
      C. H. Lam・山内博
    • Journal Title

      Communications in Mathematical Physics 277

      Pages: 237-285

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Minimum Lee weights of Type II codes over F^r_22008

    • Author(s)
      Koichi BETSUMIYA
    • Journal Title

      Discrete Mathematics 308

      Pages: 3018-3022

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On double circulant doubly even self-dual [72,86,12]codes and their neighbors.2008

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

      Australasian Journal of Combinatorics 40

      Pages: 137-144

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Determination of weight enumerators of binary extremal self-dual[42,21,8]codes.2007

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

      Finite Fields and Their Applications 14

      Pages: 177-187

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A characterization of the moonshine vertex operator algebra by means of Virasoro frames.2007

    • Author(s)
      C.H.Lam, H.Yamauchi
    • Journal Title

      International Mathematics Research Notices 1(ID rnm003,9)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hadamard matrices of order 32 and extremal ternary self-dual codes

    • Author(s)
      別宮耕一・原田昌晃・木村浩
    • Journal Title

      Designs, Codes and Cryptography (印刷中)

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Presentation] 散在型有限単純群と頂点作用素代数2010

    • Author(s)
      山内博
    • Organizer
      日本数学会2010年度年会
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2010-03-27
    • Related Report
      2010 Final Research Report
  • [Presentation] 散在型有限単純群と頂点作用素代数2010

    • Author(s)
      山内博
    • Organizer
      日本数学会2010年度年会
    • Place of Presentation
      慶慮義塾大学
    • Year and Date
      2010-03-27
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Mass formula for even codes over Z_82010

    • Author(s)
      別宮耕一
    • Organizer
      The 8th Korea-Japan Workshop on Algebra and Combinatorics
    • Place of Presentation
      浦項工科大学校(大韓民国)
    • Year and Date
      2010-02-06
    • Related Report
      2010 Final Research Report
  • [Presentation] Mass formula for even codes over Z_82010

    • Author(s)
      別宮耕一
    • Organizer
      The 8^th Korea-Japan Workshop on Algebra and Combinatorics
    • Place of Presentation
      浦項工科大学校 (大韓民国)
    • Year and Date
      2010-02-06
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Mass formula for even codes over Z_82009

    • Author(s)
      別宮耕一
    • Organizer
      Twelfth IMA International Conference on Cryptography and Coding
    • Place of Presentation
      王立農業大学(英国)
    • Year and Date
      2009-12-15
    • Related Report
      2010 Final Research Report
  • [Presentation] Mass formula for even codes over Z_82009

    • Author(s)
      別宮耕一
    • Organizer
      Twelfth IMA International Conference on Cryptography and Coding
    • Place of Presentation
      王立農業大学 (英国)
    • Year and Date
      2009-12-15
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Mass Formula for Even Codes over Z_82009

    • Author(s)
      別宮耕一
    • Organizer
      Twelfth IMA International Conference on Cryptography and Coding
    • Place of Presentation
      王立農業大学(英国)
    • Year and Date
      2009-12-15
    • Related Report
      2009 Annual Research Report
  • [Presentation] リーチ格子のフレームとその応用2009

    • Author(s)
      宗政昭弘
    • Organizer
      第54回代数学シンポジウム
    • Place of Presentation
      明治大学
    • Year and Date
      2009-08-06
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
  • [Presentation] Galois環の基底から構成される整数剰余環上の符号2009

    • Author(s)
      別宮耕一
    • Organizer
      第20回有限群論草津セミナー
    • Place of Presentation
      草津セミナーハウス(群馬県草津町)
    • Year and Date
      2009-08-02
    • Related Report
      2008 Annual Research Report
  • [Presentation] Codes over integer residue rings constructed by bases of Galois rings2009

    • Author(s)
      Koichi BETSUMIYA
    • Organizer
      Korea-Japan Workshop on Algebra and Combinatorics
    • Place of Presentation
      釜山大学(大韓民国)
    • Year and Date
      2009-02-09
    • Related Report
      2008 Annual Research Report
  • [Presentation] Codes over integer residue rings constructed by bases of Galois rings2008

    • Author(s)
      別宮耕一
    • Organizer
      The 6th Korea-Japan Workshop on Algebra and Combinatorics
    • Place of Presentation
      国立釜山大学校(大韓民国)
    • Year and Date
      2008-02-09
    • Related Report
      2010 Final Research Report
  • [Presentation] Codes over integer residue rings constructed by bases of Galois rings2008

    • Author(s)
      別宮耕一
    • Organizer
      The 6^th Korea-Japan Workshop on Algebra and Combinatorics
    • Place of Presentation
      国立釜山大学校 (大韓民国)
    • Year and Date
      2008-02-09
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Type II codes over Galois rings2007

    • Author(s)
      別宮 耕一
    • Organizer
      代数的組合せ論シンポジウム
    • Place of Presentation
      近畿大学
    • Year and Date
      2007-06-28
    • Related Report
      2007 Annual Research Report
  • [Remarks] ホームページ等

    • URL

      http://www.st.hirosaki-u.ac.jp/~betsumi/

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • URL

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

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • URL

      http://www.st.hirosaki-u.ac.jp/~betsumi/triply-even/

    • Related Report
      2010 Annual Research Report
  • [Remarks] ホームページ

    • URL

      http://www.st.hirosaki-u.ac.jp/~betsumi/

    • Related Report
      2009 Self-evaluation Report
  • [Remarks]

    • URL

      http://www.st.hirosaki-u.ac.jp/~betsumi/

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.nagoya-u.ac.jp/~koichi/

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.nagoya-U.ac.jp/~koichi/

    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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