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

Research Project

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
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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)
Keywords差集合 / デザイン / 有限幾何 / 有限群 / 相対差集合 / 群環 / 一般アダマール行列 / トランスバーサルデザイン
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.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (31 results)

All 2012 2011 2010 2009

All Journal Article (11 results) (of which Peer Reviewed: 11 results) Presentation (20 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

    • NAID

      120005660761

    • Related Report
      2011 Final Research Report
    • 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

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A construction for modified generalized Hadamard matrices using QGH matrices2012

    • Author(s)
      Y.Hiramine
    • Journal Title

      Designs, Codes and Cryptography

      Volume: 62 Issue: 3 Pages: 279-288

    • DOI

      10.1007/s10623-011-9517-x

    • NAID

      120005660761

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On (p^2,p,p^2,p)-difference sets in Zp^32012

    • Author(s)
      Y.Hiramine
    • Journal Title

      Journal of Statistical Theory and Practice

      Volume: 6 Pages: 88-96

    • Related Report
      2011 Annual Research Report
    • 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

    • NAID

      120004724832

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A family of non class-regular symmetric transversal designs of spread type2011

    • Author(s)
      Y.Hiramine
    • Journal Title

      Designs, Codes and Cryptography

      Volume: (掲載決定)

    • NAID

      120004724832

    • Related Report
      2010 Annual Research Report
    • 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

    • Related Report
      2011 Final Research Report
    • 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

    • NAID

      120005671303

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Modified generalized Hadamard matrices and constructions for transversal designs2010

    • Author(s)
      Y.Hiramine
    • Journal Title

      Designs, Codes and Cryptography

      Volume: Vol.56 Pages: 21-33

    • NAID

      120005671307

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On abelian(2n, n, 2n, 2)-difference sets2010

    • Author(s)
      Y.Hiramine
    • Journal Title

      Journal of Combinatorial Theory, Ser.A Vol.101

      Pages: 281-284

    • NAID

      120005671303

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Modified generalized Hadamard matrices and constructions for transversal designs2010

    • Author(s)
      Y.Hiramine
    • Journal Title

      Designs, Codes and Cryptography (掲載決定)

    • NAID

      120005671307

    • Related Report
      2009 Annual Research Report
    • 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
    • Related Report
      2011 Final Research Report
  • [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
    • Year and Date
      2011-12-10
    • Related Report
      2011 Annual Research Report
  • [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
    • Related Report
      2011 Final Research Report
  • [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
    • Year and Date
      2011-06-22
    • Related Report
      2011 Annual Research Report
  • [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
    • Related Report
      2011 Final Research Report
  • [Presentation] On difference matrices with respect to cosets(joint work with C.Suetke)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(招待講演)
    • Year and Date
      2011-06-01
    • Related Report
      2011 Annual Research Report
  • [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
    • Related Report
      2011 Final Research Report
  • [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
    • Year and Date
      2010-12-12
    • Related Report
      2010 Annual Research Report
  • [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
    • Related Report
      2011 Final Research Report
  • [Presentation] On TD_2(2n,n)'s admitting semiregular automorphism groups of order n^22010

    • Author(s)
      平峰豊
    • Organizer
      2010 Algebraic and Geometric Combinatorics Conference
    • Place of Presentation
      Gyeongju, South Korea
    • Year and Date
      2010-07-16
    • Related Report
      2010 Annual Research Report
  • [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
    • Related Report
      2011 Final Research Report
  • [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
    • Year and Date
      2010-06-22
    • Related Report
      2010 Annual Research Report
  • [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
    • Related Report
      2011 Final Research Report
  • [Presentation] 位数n^2の半正則自己同型群をもつTD_2(2n,n)にろいて2010

    • Author(s)
      平峰豊
    • Organizer
      有限幾何とその周辺
    • Place of Presentation
      熊本大学教育学部
    • Year and Date
      2010-05-09
    • Related Report
      2010 Annual Research Report
  • [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
    • Related Report
      2011 Final Research Report
  • [Presentation] 成分がRDSであるGH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
    • Year and Date
      2009-11-18
    • Related Report
      2009 Annual Research Report
  • [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
    • Related Report
      2011 Final Research Report
  • [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
    • Year and Date
      2009-08-07
    • Related Report
      2009 Annual Research Report
  • [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
    • Related Report
      2011 Final Research Report
  • [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
    • Year and Date
      2009-06-05
    • Related Report
      2009 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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