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

• Project/Area Number: 23540148
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kumamoto 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: ¥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.

Research Products

• [Journal Article] Demi-matroids from codes over finite Frobenius rings, Designs (2014)
  • 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
  • Peer Reviewed
• [Journal Article] The critical problem in coding theory (2013)
  • 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
• [Journal Article] Formula for the channel matrix of a certain class of (G,χ)-covariant signals (2013)
  • 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
  • Peer Reviewed
• [Journal Article] Wei-type duality theorems for matroids (2012)
  • 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
  • Peer Reviewed
• [Journal Article] A class of group covariant signal sets and its necessary and sufficient condition (2012)
  • 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
  • Peer Reviewed
• [Journal Article] Mutually disjoint 5-designs from Pless symmetry codes (2012)
  • 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
  • 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
  • Peer Reviewed
• [Journal Article] Analytical expression of s-th power of Gram matrix for group covariant signals and its application (2011)
  • Author(s): Takeshi Usuda
  • Journal Title: AIP Conference Proceedings Volume: 1363 Pages: 97-100
  • Peer Reviewed
• [Journal Article] Mutually orthogonal partial t-designs over C related to quantum jump codes (2011)
  • 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
• [Presentation] From codes to matroid and back (2014)
  • 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）
  • Invited
• [Presentation] The critical problem in coding theory (2013)
  • 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）
• [Presentation] On critical exponents of matroids and linear codes (2013)
  • 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）
• [Presentation] On critical exponents of matroids and linear codes (2013)
  • 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）
• [Presentation] Codes over rings and matroids (2011)
  • 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）
• [Presentation] Dualities in codes over rings and matroids (2011)
  • 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）
• [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）
• [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）
• [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）
• [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)
• [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）
• [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）