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Manifold research on algebraic coding theory

Research Project

Project/Area Number 20740063
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKumamoto University (2009-2011)
Aichi Prefectural University (2008)

Principal Investigator

SHIROMOTO Keisuke  Kumamoto University, 自然科学研究科, 教授 (00343666)

Research Collaborator THOMAS Britz  University of New South Wales, School of Mathematics and Statistics, Lecture
ANGATA Masayuki  株式会社デンソー, 知的財産部, 社員
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords符号理論 / 組合せデザイン / マトロイド / 自己双対符号 / 一般化ハミング重み / 双対性
Research Abstract

In this research term, I had tried to study coding theory, matroid theory, and combinatorial design theory from my past research in algebraic coding theory. Then I gave a construction of mutually disjoint designs from some codes, I found a duality theorem for matroids by using the duality in coding theory, and I introduced a new Tutte type polynomial for matroids.

Report

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

    (42 results)

All 2011 2010 2009 2008 Other

All Journal Article (16 results) (of which Peer Reviewed: 11 results) Presentation (21 results) Book (4 results) Remarks (1 results)

  • [Journal Article] Mutuallydisjoint 5-designs from Plesssymmetry codes2011

    • Author(s)
      M.Angata, K.Shiromoto
    • Journal Title

      Journal ofStatistical Theory and Practice 印刷中

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Mutually disjoint 5-designs from Pless symmetry codes2011

    • Author(s)
      M.Angata
    • Journal Title

      Journal of Statistical Theory and Practice

      Volume: (印刷中)

    • NAID

      120005399999

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 符号とマトロイドにおける双対性2010

    • Author(s)
      城本啓介
    • Journal Title

      2010年度応用数学合同研究集会報告集

      Pages: 35-36

    • Related Report
      2010 Final Research Report
  • [Journal Article] A construction of mutually disjoint Steiner systems from isomorphic Golay codes2009

    • Author(s)
      M. Jimbo and K. Shiromoto
    • Journal Title

      Journal of Combinatorial Theory, Series A

      Volume: 116 Pages: 1245-1251

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Designs from matroids2009

    • Author(s)
      T. Britz, G. Royle and K. Shiromoto
    • Journal Title

      SIAM Journal on Discrete Mathematics

      Volume: 23 Pages: 1082-1099

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Aconstruction of mutually disjointSteiner systems from isomorphic Golaycodes2009

    • Author(s)
      M. Jimbo, K. Shiromoto
    • Journal Title

      Journal of CombinatorialTheory, Series A 116

      Pages: 1245-1251

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Designs from matroids2009

    • Author(s)
      T.Britz, G.Royle, K.Shiromoto
    • Journal Title

      SIAM Journal onDiscrete Mathematics 23

      Pages: 1082-1099

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] A construction of mutually disjoint Steiner systems from isomorphic Golay codes2009

    • Author(s)
      Masakazu Jimbo
    • Journal Title

      Journal of Combinatorial Theory, Series A 116

      Pages: 1245-1251

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Designs from matroids2009

    • Author(s)
      Thomas Britz
    • Journal Title

      SIAM Journal of Discrete Mathematics 23

      Pages: 1082-1099

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A MacWilliams type identity for matroids2008

    • Author(s)
      T. Britz and K. Shiromoto
    • Journal Title

      Discrete Mathematics

      Volume: 308 Pages: 4551-4559

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] 量子ジャンプ符号の構成法について2008

    • Author(s)
      城本啓介
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1593巻 Pages: 140-144

    • Related Report
      2010 Final Research Report
  • [Journal Article] A Wei-type duality for matroids2008

    • Author(s)
      城本啓介
    • Journal Title

      第25回代数的組合せ論シンポジウム報告集

      Pages: 128-132

    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Journal Article] Pless symmetry codeから構成される互いに排反な組合せデザインについて2008

    • Author(s)
      安形昌幸、城本啓介
    • Journal Title

      2008年度応用数学合同研究集会報告集

      Pages: 51-54

    • Related Report
      2010 Final Research Report
  • [Journal Article] A MacWilliams type identity formatroids2008

    • Author(s)
      T. Britz, K. Shiromoto
    • Journal Title

      Discrete Mathematics 308

      Pages: 4551-4559

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] A MacWilliams type identity for matroids2008

    • Author(s)
      Thomas Britz
    • Journal Title

      Discrete Mathematics 308

      Pages: 4551-4559

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 量子ジャンプ符号の構成法について2008

    • Author(s)
      城本啓介
    • Journal Title

      京都大学数理解析研究所講究録 1593

      Pages: 140-144

    • Related Report
      2008 Annual Research Report
  • [Presentation] 量子情報理論と組合せデザイン2011

    • Author(s)
      城本啓介
    • Organizer
      RIMS共同研究「代数的符号理論、組合せデザインとその周辺」
    • Place of Presentation
      京都大学(京都)
    • Year and Date
      2011-03-08
    • Related Report
      2010 Final Research Report
  • [Presentation] 量子情報理論と組合せデザイン2011

    • Author(s)
      城本啓介
    • Organizer
      RIMS共同研究「代数的符号理論、組合せデザインとその周辺」
    • Place of Presentation
      京都大学 京都
    • Year and Date
      2011-03-08
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] 量子情報理論と組合せデザイン2011

    • Author(s)
      城本啓介
    • Organizer
      RIMS共同研究「代数的符号理論、組合せデザインとその周辺」
    • Place of Presentation
      京都大学、京都
    • Year and Date
      2011-03-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] 符号とマトロイドにおける双対性2010

    • Author(s)
      城本啓介
    • Organizer
      2010年度応用数学合同研究集会
    • Place of Presentation
      龍谷大学(滋賀)
    • Year and Date
      2010-12-16
    • Related Report
      2010 Final Research Report
  • [Presentation] 符号とマトロイドにおける双対性2010

    • Author(s)
      城本啓介
    • Organizer
      2010年度応用数学合同研究集会
    • Place of Presentation
      龍谷大学 滋賀
    • Year and Date
      2010-12-16
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] 符号とマトロイドにおける双対性2010

    • Author(s)
      城本啓介
    • Organizer
      2010年度応用数学合同研究集会
    • Place of Presentation
      龍谷大学、滋賀
    • Year and Date
      2010-12-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] Formula of channel matrix for coded quantum signals by classical linear codes over Zm2010

    • Author(s)
      M. Ota
    • Organizer
      2010 International Symposium on Information Theory and Its Applications
    • Place of Presentation
      Taichung(Taiwan)
    • Year and Date
      2010-10-20
    • Related Report
      2010 Final Research Report
  • [Presentation] Formula of channel matrix for coded quantum signals by classical linear codes over Zm2010

    • Author(s)
      M.Ota
    • Organizer
      2010 International Symposium on Information Theory and Its Applications
    • Place of Presentation
      Taichung, Taiwan
    • Year and Date
      2010-10-20
    • Related Report
      2010 Annual Research Report
  • [Presentation] Analytical expression of s-th power of Gram matrix for group covariant signals and its application2010

    • Author(s)
      T. S. Usuda
    • Organizer
      The Tenth International Conference on Quantum Communication, Measurement and Computation
    • Place of Presentation
      University of Queensland(Australia)
    • Year and Date
      2010-07-22
    • Related Report
      2010 Final Research Report
  • [Presentation] Analytical expression of s-th power of Gram matrix for group covariant signals and its application, The Tenth International Conference on Quantum Communication2010

    • Author(s)
      T.S.Usuda
    • Organizer
      Measurement and Computation
    • Place of Presentation
      University of Queensland, Australia
    • Year and Date
      2010-07-22
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Analytical expression of s-th power of Gram matrix for group covariant signals and its application2010

    • Author(s)
      T.S.Usuda
    • Organizer
      The Tenth International Conference on Quantum Communication, Measurement and Computation
    • Place of Presentation
      University of Queensland, Australia
    • Year and Date
      2010-07-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] A construction of mutually disjoint 5-designs from self-dual codes2008

    • Author(s)
      K. Shiromoto
    • Organizer
      The 4th International Conference on Combinatorial Mathematics and Combinatorial Computing
    • Place of Presentation
      University of Auckland(New Zealand)
    • Year and Date
      2008-12-16
    • Related Report
      2010 Final Research Report
  • [Presentation] Pless symmetry codeから構成される互いに排反な組合せデザイン2008

    • Author(s)
      安形昌幸
    • Organizer
      2008年度応用数学合同研究集会
    • Place of Presentation
      龍谷大学(滋賀)
    • Year and Date
      2008-12-16
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] A construction of mutually disjoint 5-designs from self-dual codes2008

    • Author(s)
      K.Shiromoto
    • Organizer
      The 4th International Conference on Combinatorial Mathematics and Combinatorial Computing
    • Place of Presentation
      University of Auckland, New Zealand
    • Year and Date
      2008-12-16
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] A construction of mutually disjoint 5-designs from self-dual codes2008

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      The 4th International Conference on Combinatorial Mathematics and Combinatorial Computing
    • Place of Presentation
      Auckland (New Zealand)
    • Year and Date
      2008-12-16
    • Related Report
      2008 Annual Research Report
  • [Presentation] 自己双対符号から構成されるt-SEEDについて2008

    • Author(s)
      城本啓介
    • Organizer
      RIMS共同研究「代数的符号理論と組合せデザイン」
    • Place of Presentation
      京都大学数理解析研究所(京都)
    • Year and Date
      2008-10-14
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] デザイン構造をもつマトロイド2008

    • Author(s)
      城本啓介
    • Organizer
      研究集会「離散数学の統計科学および関連分野への応用」
    • Place of Presentation
      ホテルくさかべアルメリア(岐阜)
    • Year and Date
      2008-09-17
    • Related Report
      2010 Final Research Report
  • [Presentation] デザイン構造をもつマトロイド2008

    • Author(s)
      城本啓介
    • Organizer
      研究集会「離散数学の統計科学および関連分野への応用」
    • Place of Presentation
      ホテルくさかベアルメリア(岐阜)
    • Year and Date
      2008-09-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] 互いに素な組合せデザインについて2008

    • Author(s)
      安形昌幸
    • Organizer
      純粋数学及び応用数学としての組合せ論・離散数学そしてその周辺ワークショップ
    • Place of Presentation
      電気通信大学(東京)
    • Year and Date
      2008-07-05
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] A Wei-type duality theorem for matroids2008

    • Author(s)
      城本啓介
    • Organizer
      第25回代数的組合せ論シンポジウム
    • Place of Presentation
      北海道大学(北海道)
    • Year and Date
      2008-06-24
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] A Wei-type duality theoremfor matroids2008

    • Author(s)
      城本啓介
    • Organizer
      第25回代数的組合せ論シンポジウム
    • Place of Presentation
      北海道大学、北海道
    • Year and Date
      2008-06-24
    • Related Report
      2010 Self-evaluation Report
  • [Book] Information Security, Coding Theory and Related Combinatorics2011

    • Author(s)
      D. Crnkovic
    • Publisher
      Ios Press
    • Related Report
      2010 Final Research Report
  • [Book] Information Security, Coding Theoryand Related Combinatorics2011

    • Author(s)
      D.Crnkovic
    • Publisher
      Ios Press
    • Related Report
      2010 Self-evaluation Report
  • [Book] Information Security, Coding Theory and Related Combinatorics2011

    • Author(s)
      D.Crnkovic
    • Publisher
      Ios Press
    • Related Report
      2010 Annual Research Report
  • [Book] 暗号とセキュリティ2010

    • Author(s)
      神保雅一
    • Publisher
      オーム社
    • Related Report
      2010 Annual Research Report 2010 Self-evaluation Report 2010 Final Research Report
  • [Remarks]

    • URL

      http://www.srik.kumamoto-u.ac.jp/

    • Related Report
      2010 Final Research Report

URL: 

Published: 2008-04-01   Modified: 2017-05-19  

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