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2011 Fiscal Year Final Research Report

Research on semiregular relative difference sets of(u,λ)-type

Research Project

  • PDF
Project/Area Number 21540021
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

HIRAMINE Yutaka  熊本大学, 教育学部, 教授 (30116173)

Co-Investigator(Renkei-kenkyūsha) CHIGIRA Naoki  熊本大学, 自然科学研究科, 准教授 (40292073)
WATANABE Atsumi  熊本大学, 自然科学研究科, 教授 (90040120)
Project Period (FY) 2009 – 2011
Keywords差集合 / デザイン / 有限幾何 / 有限群
Research Abstract

A. Blokhuis et al. have shown that abelian semiregular relative difference sets with lambda=1 are p-groups for some prime p. In this research we study the case lambda=2 and show that the corresponding groups are 2-groups with some exceptions. Concerning the group G=Zp×Zp×Zp, we characterize the known semiregular relative difference sets in G by using functions from Zp to Zp. We also consider generalized Hadamard matrices and give their modification. As an application we construct new generalized Hadamard matrices related to spreads.

  • Research Products

    (15 results)

All 2012 2011 2010 2009

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (10 results)

  • [Journal Article] A construction for modified generalized Hadamard matrices using QGH matrices2012

    • Author(s)
      平峰豊
    • Journal Title

      Designs, Codes and Cryptography

      Volume: vol.62 Pages: 279-288

    • Peer Reviewed
  • [Journal Article] On(p^2, p, p^2, p)-difference sets in Zp^32012

    • Author(s)
      平峰豊
    • Journal Title

      Journal of Statistical Theory and Practice

      Volume: vol.6 Pages: 88-96

    • Peer Reviewed
  • [Journal Article] A family of non class regular symmetric transversal designs of spread type2011

    • Author(s)
      平峰豊
    • Journal Title

      Designs, Codes and Cryptography

      Volume: Vol.60 Pages: 91-99

    • Peer Reviewed
  • [Journal Article] Modified generalized Hadamard matrices and constructions for transversal desig ns2010

    • Author(s)
      平峰豊
    • Journal Title

      Designs, Codes and Cryptography

      Volume: Vol.56 Pages: 21-33

    • Peer Reviewed
  • [Journal Article] On abelian(2n, n, 2n, 2)-difference sets2010

    • Author(s)
      平峰豊
    • Journal Title

      Journal of Combinatorial Theory, Ser. A

      Volume: Vol.101 Pages: 281-284

    • Peer Reviewed
  • [Presentation] Modified difference matricesとFrobenius群2011

    • Author(s)
      平峰豊
    • Organizer
      有限幾何とその周辺
    • Place of Presentation
      大分大学(大分)
    • Year and Date
      2011-12-10
  • [Presentation] Cosetsに関するdifference matricesについて(末竹千博との共同研究)2011

    • Author(s)
      平峰豊
    • Organizer
      代数的組合せ論シンポジウム
    • Place of Presentation
      大分大学(大分)
    • Year and Date
      2011-06-22
  • [Presentation] On difference matrices with respect to cosets(joint work with C. Suetake)2011

    • Author(s)
      平峰豊
    • Organizer
      Institute of Mathematical Science of National University of Singapore, Coding, Cryptology and Combinatorial Designs
    • Place of Presentation
      Singapore
    • Year and Date
      2011-06-01
  • [Presentation] 変形一般アダマール行列を用いたGH(q, 4m)の構成について2010

    • Author(s)
      平峰豊
    • Organizer
      Hadamard行列とそれに関係する代数的組合せ論
    • Place of Presentation
      神戸学院大学(兵庫)
    • Year and Date
      2010-12-12
  • [Presentation] On TD_2(2n, n)'s admitting semiregular automorphism groups of order n^22010

    • Author(s)
      平峰豊
    • Organizer
      2010Algebraic and Geometric Combinatorics Conference
    • Place of Presentation
      Gyeongju, South Korea(韓国)
    • Year and Date
      2010-07-16
  • [Presentation] On TD_2(2n, n)'s admitting semiregular automorphism groups of order n^22010

    • Author(s)
      平峰豊
    • Organizer
      代数的組合せ論シンポジウム
    • Place of Presentation
      高知大学(高知)
    • Year and Date
      2010-06-22
  • [Presentation] 位数n^2の半正則自己同型群をもつTD_2(2n, n)について2010

    • Author(s)
      平峰豊
    • Organizer
      有限幾何とその周辺
    • Place of Presentation
      熊本
    • Year and Date
      2010-05-09
  • [Presentation] 成分がRDSである一般アダマール行列の構成2009

    • Author(s)
      平峰豊
    • Organizer
      代数的組合せ論および関連する群と代数
    • Place of Presentation
      信州大学理学部(長野)
    • Year and Date
      2009-11-18
  • [Presentation] RDSと一般変形アダマール行列2009

    • Author(s)
      平峰豊
    • Organizer
      有限幾何とその周辺
    • Place of Presentation
      東京女子大学(東京)
    • Year and Date
      2009-08-07
  • [Presentation] 変形一般アダマール行列について2009

    • Author(s)
      平峰豊
    • Organizer
      代数的組み合わせ論シンポジウム
    • Place of Presentation
      山形県生涯学習センター(山形)
    • Year and Date
      2009-06-05

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Published: 2013-07-31  

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