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2004 Fiscal Year Final Research Report Summary

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

Research Project

Project/Area Number 14540004
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

OZEKI Michio  Yamagata University, Faculty of Science, Department of Mathematical Sciences, Professor, 理学部, 教授 (90087073)

Co-Investigator(Kenkyū-buntansha) KITAZUME Masaaki  Chiba University, Faculty of Science, Professor, 理学部, 教授 (60204898)
MUNEMASA Akihiro  Tohoku University, Graduate School of Information Science, Professor, 大学院・情報科学研究科, 教授 (50219862)
HARADA Masaaki  Yamagata University, Faculty of Science, Department of Mathematical Sciences, Associate Professor, 理学部, 助教授 (90292408)
SAWADA Hideki  Yamagata University, Networking and Computing Service Center, Professor, 学術情報基盤センター, 教授 (30095856)
MURABAYASHI Naoki  Yamagata University, Faculty of Science, Department of Mathematical Sciences, Associate Professor, 理学部, 助教授 (80261676)
Project Period (FY) 2002 – 2004
KeywordsCoding theory / lattice / Jacobi form / Siegel modular forms
Research Abstract

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.

  • Research Products

    (12 results)

All 2005 2004 2003 2002

All Journal Article (12 results)

  • [Journal Article] On QM-abelian surfaces with model of GL_2-type over Q2005

    • Author(s)
      N.Murabayashi
    • Journal Title

      Journal of Number Theory 112

      Pages: 116-188

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On QM-abelian surfaces with model of GL_2-type over Q2005

    • Author(s)
      N.Murabayashi
    • Journal Title

      Journal of Number Theory Vol.112

      Pages: 116-188

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Covering radius problems for ternary self-dual codes.2004

    • Author(s)
      M.Harada, M.Ozeki, K.Tanabe
    • Journal Title

      Design, Codes and Cryptology 33

      Pages: 149-158

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Covering radius problems for ternary self-dual codes2004

    • Author(s)
      M.Harada, M.Ozeki, K.Tanabe
    • Journal Title

      Design, Codes and Cryptology Vol.33

      Pages: 149-158

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Note on the shadow process in coding theory2003

    • Author(s)
      M.Ozeki
    • Journal Title

      Discrete Mathematics 264

      Pages: 187-200

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Note on the shadow process in coding theory2003

    • Author(s)
      M.Ozeki
    • Journal Title

      Discrete Mathematics Vol.264

      Pages: 187-200

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Covering radius problem for singly even self-dual binary codes.2002

    • Author(s)
      M.Ozeki
    • Journal Title

      IEEE Transaction on Information Theory 48

      Pages: 547-557

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Ternary code construction of odd unimodular extremal lattices.2002

    • Author(s)
      M.Harada, M.Kitazume, M.Ozeki
    • Journal Title

      Journal of Algebraic Combinatorics 16

      Pages: 209-223

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Even unimodular Gaussian lattices of rank 122002

    • Author(s)
      A.Kitazume, A.Munemasa
    • Journal Title

      Journal of Number Theory 95

      Pages: 77-94

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Covering radius problem for singly even self dual binary codes2002

    • Author(s)
      M.Ozeki
    • Journal Title

      IEEE Transaction on Information Theory Vol.48

      Pages: 547-557

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Tertiary code construction of odd unimodular extremal lattices2002

    • Author(s)
      M.Harada, M.Kitazume, M.Ozeki
    • Journal Title

      Journal of Algebraic Combinatorics Vol.16

      Pages: 209-223

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Even unimodular Gaussian lattices of rank 122002

    • Author(s)
      A.Kitazume, A.Munemasa
    • Journal Title

      Journal of Number Theory Vol.95

      Pages: 77-94

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2006-07-11  

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