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Some problems in combinatorial theory and quantum information theory based on algebraic coding theory

Research Project

Project/Area Number 23540148
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKumamoto University

Principal Investigator

SHIROMOTO Keisuke  熊本大学, 自然科学研究科, 教授 (00343666)

Co-Investigator(Renkei-kenkyūsha) JIMBO Masakazu  名古屋大学, 大学院情報科学研究科, 教授 (50103049)
USUDA Tsuyoshi  愛知県立大学, 情報科学部, 准教授 (80273308)
CHIGIRA Naoki  熊本大学, 大学院自然科学研究科, 准教授 (40292073)
Project Period (FY) 2011 – 2014
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords符号 / マトロイド / 組合せデザイン / 量子符号 / 組合せ論 / 符号理論 / 量子情報理論
Outline of Final Research Achievements

In algebraic coding theory, I have studied mainly the existence problem and the construction problem of codes. Based on these problems, I tried to consider a kind of the similar problems in matroid theory, combinatorial design theory, and quantum information theory in this research period. One of the main results is to give a construction of matroids from codes over finite rings.

Report

(4 results)
  • 2014 Final Research Report ( PDF )
  • 2013 Annual Research Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (21 results)

All 2014 2013 2012 2011 Other

All Journal Article (9 results) (of which Peer Reviewed: 7 results) Presentation (12 results) (of which Invited: 1 results)

  • [Journal Article] Demi-matroids from codes over finite Frobenius rings, Designs2014

    • Author(s)
      Thomas Britz, Keisuke Shiromoto,Thomas Westerback
    • Journal Title

      Codes, and Cryptography

      Volume: 未定 Issue: 1 Pages: 97-107

    • DOI

      10.1007/s10623-013-9895-3

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The critical problem in coding theory2013

    • Author(s)
      Keisuke Shiromoto
    • Journal Title

      第30回代数的組合せ論シンポジウム報告集

      Volume: - Pages: 80-85

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Formula for the channel matrix of a certain class of (G,χ)-covariant signals2013

    • Author(s)
      Y. Ishikawa, K. Shiromoto, T. S. Usuda
    • Journal Title

      13th Asian Quantum Information Science Conference (AQIS2013), Chennai, India, Extended Abstracts of AQIS2013

      Volume: - Pages: 209-210

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Wei-type duality theorems for matroids2012

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

      Designs, Codes and Cryptography

      Volume: 62 Issue: 3 Pages: 331-341

    • DOI

      10.1007/s10623-011-9524-y

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] A class of group covariant signal sets and its necessary and sufficient condition2012

    • Author(s)
      T. S. Usuda
    • Journal Title

      Abstracts of Papers of 11th International Conference on Quantum Communication, Measurement and Computing

      Volume: P3-57 Pages: 361-361

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Mutually disjoint 5-designs from Pless symmetry codes2012

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

      Journal of Statistical Theory and Practice

      Volume: 6 Issue: 1 Pages: 78-87

    • DOI

      10.1080/15598608.2012.647525

    • NAID

      120005399999

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] 整数環上の任意の線形符号による量子信号系の通信路行列の解析解2012

    • Author(s)
      太田 征輝
    • Journal Title

      電子情報通信学会論文誌

      Volume: J95-B, No.2 Pages: 110-118

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Analytical expression of s-th power of Gram matrix for group covariant signals and its application2011

    • Author(s)
      Takeshi Usuda
    • Journal Title

      AIP Conference Proceedings

      Volume: 1363 Pages: 97-100

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Mutually orthogonal partial t-designs over C related to quantum jump codes2011

    • Author(s)
      神保 雅一
    • Journal Title

      第28回代数的組合せ論シンポジウム報告集

      Volume: - Pages: 76-81

    • Related Report
      2011 Research-status Report
  • [Presentation] From codes to matroid and back2014

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      The 3rd Taiwan-Japan Conference on Combinatorics and its Applications (3TJCCA)
    • Place of Presentation
      National Chiayi University(Chiayi City, Taiwan)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] The critical problem in coding theory2013

    • Author(s)
      城本 啓介
    • Organizer
      第30回代数的組合せ論シンポジウム
    • Place of Presentation
      静岡大学(静岡県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] On critical exponents of matroids and linear codes2013

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      Designs, Codes, Graphs and Related Areas
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Related Report
      2013 Annual Research Report
  • [Presentation] On critical exponents of matroids and linear codes2013

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      37th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing (37ACCMCC)
    • Place of Presentation
      The University of Western Australia(Perth, Australia)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Codes over rings and matroids2011

    • Author(s)
      城本 啓介
    • Organizer
      研究集会「離散数理構造とその応用」
    • Place of Presentation
      名古屋大学(愛知)
    • Related Report
      2011 Research-status Report
  • [Presentation] Dualities in codes over rings and matroids2011

    • Author(s)
      城本 啓介
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      龍谷大学(滋賀)
    • Related Report
      2011 Research-status Report
  • [Presentation] 整数環上の様々な線形符号による相互情報量の特性2011

    • Author(s)
      太田 征輝
    • Organizer
      第34回情報理論とその応用シンポジウム
    • Place of Presentation
      ホテル森の風鶯宿(岩手)
    • Related Report
      2011 Research-status Report
  • [Presentation] (G,χ)-共変的量子信号とその必要十分条件2011

    • Author(s)
      石川 喜啓
    • Organizer
      第34回情報理論とその応用シンポジウム
    • Place of Presentation
      ホテル森の風鶯宿(岩手)
    • Related Report
      2011 Research-status Report
  • [Presentation] The critical problem for graphs, matroids, and codes

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      The 2nd Japan-Taiwan Conference on Combinatorics and its Applications
    • Place of Presentation
      名古屋大学(愛知)
    • Related Report
      2012 Research-status Report
  • [Presentation] Codes over rings and matroids

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      The 36th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing
    • Place of Presentation
      University of New South Wales (Sydney, Australia)
    • Related Report
      2012 Research-status Report
  • [Presentation] 4元自己双対符号を用いた互いに排反な組合せデザインの構成について

    • Author(s)
      穴井佑弥
    • Organizer
      第35回情報理論とその応用シンポジウム
    • Place of Presentation
      別府湾ロイヤルホテル(大分)
    • Related Report
      2012 Research-status Report
  • [Presentation] 古典-量子通信における通信路行列公式の一般化に向けて

    • Author(s)
      石川喜啓
    • Organizer
      第35回情報理論とその応用シンポジウム
    • Place of Presentation
      別府湾ロイヤルホテル(大分)
    • Related Report
      2012 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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