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Matroids, Quantum Information Theory, and Codes

Research Project

Project/Area Number 26400187
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionKumamoto University

Principal Investigator

Keisuke Shiromoto  熊本大学, 大学院先端科学研究部(工), 教授 (00343666)

Co-Investigator(Kenkyū-buntansha) 千葉 周也  熊本大学, 大学院先端科学研究部(工), 講師 (80579764)
Co-Investigator(Renkei-kenkyūsha) USUDA Tsuyoshi  愛知県立大学, 情報科学部, 教授 (80273308)
CHIGIRA Naoki  熊本大学, 大学院先端科学研究部, 准教授 (40292073)
Research Collaborator Thomas Britz  University of New South Wales, School of Mathematics, Senior Lecturer
Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywordsマトロイド / 量子情報 / 線形符号 / 符号理論 / 量子情報理論 / 組合せ論
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 and quantum information theory in this research period. The main results contain a classification theorem and an upper bound on critical exponents of any representative matroids over finite fields and a classification result on the critical exponent of a Dowling matroid over a finite field.

Report

(4 results)
  • 2017 Final Research Report ( PDF )
  • 2016 Annual Research Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (40 results)

All 2017 2016 2015 2014 Other

All Int'l Joint Research (4 results) Journal Article (12 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 9 results,  Acknowledgement Compliant: 6 results,  Open Access: 3 results) Presentation (23 results) (of which Int'l Joint Research: 9 results,  Invited: 5 results) Remarks (1 results)

  • [Int'l Joint Research] University of New South Wales(Australia)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] University of Tromso(Norway)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] University of New South Wales(Australia)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] University of Tromso(Norway)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Degree sum conditions for vertex-disjoint cycles passing through specified vertices2017

    • Author(s)
      Shuya Chiba, Tomoki Yamashita
    • Journal Title

      Discrete Mathematics

      Volume: 340 Issue: 4 Pages: 678-690

    • DOI

      10.1016/j.disc.2016.12.010

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On dominating even subgraphs in cubic graphs2017

    • Author(s)
      Roman Cada, Shuya Chiba, Kenta Ozeki, Kiyoshi Yoshimoto
    • Journal Title

      SIAM Journal on Discrete Mathematics

      Volume: -

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] On the covering dimension of a linear code2016

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

      IEEE Transaction on Information Theory

      Volume: 62 Issue: 5 Pages: 2694-2701

    • DOI

      10.1109/tit.2016.2538768

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] A generalization of Kung’s theorem2016

    • Author(s)
      Trygve Johnsen, Keisuke Shiromoto, Hugues Verdure
    • Journal Title

      Designs, Codes and Cryptography

      Volume: - Issue: 1 Pages: 169-178

    • DOI

      10.1007/s10623-015-0139-6

    • Related Report
      2016 Annual Research Report 2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] emarks on upper and lower bounds for matching sequencibility of graphs2016

    • Author(s)
      Shuya Chiba, Yuji Nakano
    • Journal Title

      FILOMAT

      Volume: 30 Issue: 8 Pages: 2091-2099

    • DOI

      10.2298/fil1608091c

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] 二部グラフ上の完全マッチングを含む2-因子と有向グラフ上の有向2-因子2016

    • Author(s)
      千葉 周也, 山下 登茂紀
    • Journal Title

      2016年度応用数学合同研究集会報告集

      Volume: - Pages: 122-129

    • Related Report
      2016 Annual Research Report
    • Acknowledgement Compliant
  • [Journal Article] Vertex-disjoint subgraphs with high degree sums2015

    • Author(s)
      Shuya Chiba, Nicolas Lichiardopol
    • Journal Title

      Electronic Notes in Discrete Mathematics

      Volume: 49 Pages: 359-366

    • DOI

      10.1016/j.endm.2015.06.050

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] On lower bounds for matching sequencibility of general graphs2015

    • Author(s)
      Shuya Chiba
    • Journal Title

      Proceedings of The 2015 Engineering Workshop among Ajou University, Shandong University and Kumamoto University

      Volume: - Pages: 52-52

    • Related Report
      2015 Research-status Report
  • [Journal Article] A note on a basic exact sequence for the Lee and Euclidean weights of linear codes2015

    • Author(s)
      Minjia Shi, Keisuke Shiromoto, Patrick Sole
    • Journal Title

      Linear Algebra and its Applications

      Volume: 未定 Pages: 151-153

    • DOI

      10.1016/j.laa.2015.01.033

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] On critical exponents of matroids and linear codes2014

    • Author(s)
      Keisuke Shiromoto
    • Journal Title

      数理解析研究所講究録

      Volume: 1889

    • Related Report
      2014 Research-status Report
  • [Journal Article] Group covariance and formula of channel matrix of coded 4PSK signals by linear codes over F_42014

    • Author(s)
      M. Tanaka, T. Sogabe, K. Shiromoto, and T. S. Usuda
    • Journal Title

      2014 International Symposium on Information Theory and Its Applications (ISITA2014)

      Volume: - Pages: 348-348

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Formula of channel matrix for covariant signal set with respect to a direct product of groups2014

    • Author(s)
      T. S. Usuda, T. Sogabe, and K. Shiromoto
    • Journal Title

      12th International Conference on Quantum Communication, Measurement and Computing (QCMC2014)

      Volume: - Pages: 45-45

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Presentation] 符号理論的マトロイド理論へのいざない2017

    • Author(s)
      城本 啓介
    • Organizer
      筑波大学組合せ論・情報理論セミナー
    • Place of Presentation
      筑波大学(茨城県つくば市)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] 符号理論的マトロイド理論について2017

    • Author(s)
      城本 啓介
    • Organizer
      近畿大学数学教室講演会
    • Place of Presentation
      近畿大学(大阪府東大阪市)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Critical problem for matroids and codes2017

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      Discrete Mathematics Research Group meeting
    • Place of Presentation
      Monash University (Melbourne, Australia)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] 次数条件と2-因子について2016

    • Author(s)
      千葉周也
    • Organizer
      RIMS 共同研究「閉曲面上のグラフの彩色問題への因子・閉路を利用してのアプローチ」
    • Place of Presentation
      京都大学数理解析研究所(京都府京都市)
    • Year and Date
      2016-03-07
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Critical problem in coding theory2016

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      The 4th Japan-Taiwan Conference on Combinatorics and its Applications
    • Place of Presentation
      北九州国際会議場(福岡県北九州市)
    • Year and Date
      2016-03-05
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Degree conditions for 2-factors with k cycles in bipartite graphs2016

    • Author(s)
      Shuya Chiba
    • Organizer
      The 4th Japan-Taiwan Conference on Combinatorics and its Applications
    • Place of Presentation
      北九州国際会議場(福岡県北九州市)
    • Year and Date
      2016-03-05
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] On 2-factors with k cycles in graphs2016

    • Author(s)
      千葉周也
    • Organizer
      Hakata Workshop 2016 - Discrete Mathematics and its Applications
    • Place of Presentation
      九州大学(福岡県福岡市)
    • Year and Date
      2016-02-23
    • Related Report
      2015 Research-status Report
  • [Presentation] On the covering number of matroids2016

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      The Japanese Conference on Combinatorics and its Applications (JCCA 2016)
    • Place of Presentation
      Kyoto University, Clock Tower Centennial Hall (Kyoto, Japan)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On the covering number of matroids2016

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      The 40th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing (40ACCMCC)
    • Place of Presentation
      University of Newcastle (Newcastle, Australia)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On 2-factors through specified perfect matchings in bipartite graphs2016

    • Author(s)
      Shuya Chiba
    • Organizer
      The Japanese Conference on Combinatorics and its Applications (JCCA 2016)
    • Place of Presentation
      Kyoto University, Clock Tower Centennial Hall (Kyoto, Japan)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 二部グラフ上の完全マッチングを含む2-因子と有向グラフ上の有向2-因子2016

    • Author(s)
      千葉 周也, 山下 登茂紀
    • Organizer
      2016年度応用数学合同研究集会
    • Place of Presentation
      龍谷大学(滋賀県大津市)
    • Related Report
      2016 Annual Research Report
  • [Presentation] Critical exponents of Dowling matroids2015

    • Author(s)
      古賀義孝
    • Organizer
      2015年度応用数学合同研究集会
    • Place of Presentation
      龍谷大学(滋賀県大津市)
    • Year and Date
      2015-12-17
    • Related Report
      2015 Research-status Report
  • [Presentation] Codes from complete bipartite graphs and 3-regular graphs2015

    • Author(s)
      Shunpei Yamaguchi
    • Organizer
      39th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing
    • Place of Presentation
      University of Queensland (Brisbane, Australia)
    • Year and Date
      2015-12-07
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Critical exponents of Dowling matroids2015

    • Author(s)
      Yoshitaka Koga
    • Organizer
      39th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing
    • Place of Presentation
      University of Queensland (Brisbane, Australia)
    • Year and Date
      2015-12-07
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] On lower bounds for matching sequencibility of general graphs2015

    • Author(s)
      Shuya Chiba
    • Organizer
      The 2015 Engineering Workshop among Ajou University, Shandong University and Kumamoto University
    • Place of Presentation
      Kumamoto University (Kumamoto, Japan)
    • Year and Date
      2015-11-12
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] On covering dimension of linear codes and matroids2015

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      25th British Combinatorial Conference
    • Place of Presentation
      University of Warwick (Coventry, UK)
    • Year and Date
      2015-07-06
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] On the covering dimension of a linear code2015

    • Author(s)
      城本 啓介
    • Organizer
      研究集会「有限幾何と組合せデザイン」
    • Place of Presentation
      東京理科大学、東京都
    • Year and Date
      2015-03-06 – 2015-03-07
    • Related Report
      2014 Research-status Report
  • [Presentation] グラフにおける次数条件と点素な閉路2015

    • Author(s)
      千葉 周也
    • Organizer
      第11回組合せ論若手研究集会
    • Place of Presentation
      慶應義塾大学、東京都
    • Year and Date
      2015-03-06
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] On the critical exponent of a linear code and a matroid2015

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      The 13th Japan-Korea Workshop on Algebra and Combinatorics
    • Place of Presentation
      九州工業大学、福岡県
    • Year and Date
      2015-01-29 – 2015-01-31
    • Related Report
      2014 Research-status Report
  • [Presentation] On the covering dimensions of a linear code and its relation to matroids2014

    • Author(s)
      Keisuke Shiromoto
    • Organizer
      38th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing (38ACCMCC)
    • Place of Presentation
      Victoria University of Wellington, Wellington, New Zealand
    • Year and Date
      2014-12-01 – 2014-12-05
    • Related Report
      2014 Research-status Report
  • [Presentation] Some remarks on upper and lower bounds for matching sequencibility of graphs2014

    • Author(s)
      Shuya Chiba
    • Organizer
      The First Sino-Japan Symposium on Graph Theory, Combinatorics and their Applications
    • Place of Presentation
      Academy of Mathematics and Systems Science, Beijing, China
    • Year and Date
      2014-10-30
    • Related Report
      2014 Research-status Report
  • [Presentation] 正則グラフの Matching Sequencibility について2014

    • Author(s)
      千葉 周也
    • Organizer
      離散数学とその応用研究集会2014
    • Place of Presentation
      新潟総合テレビ・ゆめディア、新潟県
    • Year and Date
      2014-08-20
    • Related Report
      2014 Research-status Report
  • [Presentation] Matching sequencibility of regular graphs2014

    • Author(s)
      千葉 周也
    • Organizer
      第31回代数的組合せ論シンポジウム
    • Place of Presentation
      東北大学、宮城県
    • Year and Date
      2014-06-19
    • Related Report
      2014 Research-status Report
  • [Remarks] 熊本大学工学部数理工学科ホームページ

    • URL

      http://www.srik.kumamoto-u.ac.jp

    • Related Report
      2016 Annual Research Report 2015 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2019-04-17  

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