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

Algebraic coding theory and combinatorial designs

Research Project

Project/Area Number 20540103
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

HARADA Masaaki  Yamagata University, 理学部, 准教授 (90292408)

Co-Investigator(Kenkyū-buntansha) MUNEMASA Akihiro  東北大学, 大学院・情報科学研究科, 教授 (50219862)
Co-Investigator(Renkei-kenkyūsha) KITAZUME Masaaki  千葉大学, 大学院・理学研究科, 教授 (60204898)
ARAYA Makoto  静岡大学, 情報学部, 准教授 (70303526)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords組合せ論 / 自己双対符号 / 組合せデザイン / 格子
Research Abstract

The main aim of this research is to study self-dual codes, which are of interest from an algebraic point of view. In self-dual codes, it is a fundamental problem to classify these codes. We completed classifications of several types of self-dual codes using some different approaches. We constructed extremal self-dual codes which have the largest minimum weights among all self-dual codes of that length. Using self-dual codes, we also studied combinatorial designs.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (24 results)

All 2010 2009 2008 Other

All Journal Article (19 results) (of which Peer Reviewed: 18 results) Presentation (5 results)

  • [Journal Article] Extremal Type II Z_4-codes of lengths 56 and 642010

    • Author(s)
      M.Harada
    • Journal Title

      J.Combin.Theory Ser.A 117

      Pages: 1285-1288

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] An upper bound on the minimum weight of Type II Z_<2k>-codes2010

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

      J.Combin.Theory Ser.A 118

      Pages: 190-196

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Classification of generalized Hadamard matrices H(6, 3) and quaternary Hermitian self-dual codes of length 182010

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

      Electronic J.Combin. 17

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Extremal Type II Z 4-codes of lengths 56 and 642010

    • Author(s)
      M.Harada
    • Journal Title

      J.Combin.Theory Ser.A

      Volume: 117 Pages: 1285-1288

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An upper bound on the minimum weight of Type II Z 2k-codes2010

    • Author(s)
      M.Harada
    • Journal Title

      J.Combin.Theory Ser.A

      Volume: 118 Pages: 190-196

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Classification of generalized Hadamard matrices H(6, 3) and quaternary Hermitian self-dual codes of length 182010

    • Author(s)
      C.Lam
    • Journal Title

      Electronic J.Combin.

      Volume: 17

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the classification of self-dual Z_k-codes2009

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

      Lecture Notes Comput.Sci. 5921

      Pages: 78-90

    • Related Report
      2010 Final Research Report
  • [Journal Article] Classification of ternary extremal self-dual codes of length 282009

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

      Mathematics of Comput. 78

      Pages: 1787-1796

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A complete classification of ternary self-dual codes of length 242009

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

      J.Combin.Theory Ser.A 116

      Pages: 1063-1072

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the existence of frames of the Niemeier lattices and self-dual codes over Fp2009

    • Author(s)
      M.Harada
    • Journal Title

      J.Algebra 321

      Pages: 2345-2352

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] There exists no self-dual [24, 12, 10] code over F_52009

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

      Designs, Codes and Cryptogr. 52

      Pages: 125-127

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A complete classification of ternary self-dual codes of length 242009

    • Author(s)
      M.Harada
    • Journal Title

      J.Combin.Theory Ser.A 116

      Pages: 1063-1072

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Classification of ternary extremal self-dual codes of length 282009

    • Author(s)
      M.Harada
    • Journal Title

      Mathematics of Computation 78

      Pages: 1787-1796

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the classification of self-dual Zk-codes2009

    • Author(s)
      M.Harada
    • Journal Title

      Lecture Notes in Comput.Sci. 5921

      Pages: 78-90

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the existence of frames of the Niemeier lattices and self-dual codes over Fp2009

    • Author(s)
      M. Harada
    • Journal Title

      J. Algebra 321

      Pages: 2345-2352

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

    • Author(s)
      M. Harada
    • Journal Title

      Designs, Codes and Cryptogr 52

      Pages: 125-127

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An extremal doubly even self-dual code of length 1122008

    • Author(s)
      M. Harada
    • Journal Title

      Electronic J. Combin 15(Electronic)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The twisted Grassmann graph is the block graph of a design

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

      Innov.Incidence Geom. (掲載決定)

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Classification of quaternary Hermitian self-dual codes of length 20

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

      IEEE Trans.Inform.Theory (掲載決定)

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Presentation] 自己双対符号とその周辺2010

    • Author(s)
      原田昌晃
    • Organizer
      第55回代数学シンポジウム
    • Place of Presentation
      北海道大学
    • Year and Date
      2010-08-12
    • Related Report
      2010 Final Research Report
  • [Presentation] Extremal Type II Z_<2k>-codes2009

    • Author(s)
      原田昌晃
    • Organizer
      代数学と計算
    • Place of Presentation
      首都大学東京
    • Year and Date
      2009-12-02
    • Related Report
      2010 Final Research Report
  • [Presentation] Twisted Grassmann graph is the block graph of a design2009

    • Author(s)
      宗政昭弘
    • Organizer
      Summer School on Designs and Codes
    • Place of Presentation
      ヒルズサンピア山形
    • Year and Date
      2009-06-21
    • Related Report
      2010 Final Research Report
  • [Presentation] On the classification of extremal Type II Z_4-codes of length 242009

    • Author(s)
      原田昌晃
    • Organizer
      Korea-Japan Workshop on Algebra and Combinatorics
    • Place of Presentation
      Pusan National University、韓国
    • Year and Date
      2009-02-09
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] Self-dual codeの分類について2008

    • Author(s)
      原田昌晃
    • Organizer
      離散数学とその応用研究集会
    • Place of Presentation
      茨城大学
    • Year and Date
      2008-08-21
    • Related Report
      2010 Final Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi