Research on triply even codes and their related mathematical structures

• Project/Area Number: 26400002
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Hirosaki University
• Principal Investigator: Betsumiya Koichi 弘前大学, 理工学研究科, 准教授 (60364684)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 群論 / 代数的組合せ論 / 頂点作用素代数 / 代数的符号理論

Outline of Final Research Achievements

1. We have constructed maximal triply even codes from the Witt design and Higman design respectively. The automorphism groups are the Mathieu group M22.2 and the Higman sims group HS respectively. 2. We have constructed maximal triply even codes from the Hamming graphs and have constructed their weight enumerators generally. 3. We have constructed a infinite series of triply even codes from a kind of finite geometries and have confirmed their maximality in a possible range by computers.

Research Products

• [Journal Article] Triply even codes constructed from distance regular graphs (2016)
  • Author(s): 別宮耕一
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 2003 Pages: 66-73
  • Open Access
• [Presentation] Maximal triply even codes constructed from finite geometries (2016)
  • Author(s): 別宮耕一
  • Organizer: 研究集会「実験計 画法と符号および関連する組合せ構造」
  • Place of Presentation: 秋保リゾートホテルクレセント（宮城県仙台市）
  • Year and Date: 2016-11-28
  • Invited
• [Presentation] Triply even codes related to simple groups (2016)
  • Author(s): Koichi Betsumiya
  • Organizer: Workshop on Finite Groups, VOA, and algebraic combinatorics
  • Place of Presentation: Foguang University
  • Year and Date: 2016-03-22
  • Int'l Joint Research
• [Presentation] Triply even codes constructed from distance regular graphs (2016)
  • Author(s): 別宮 耕一
  • Organizer: 代数的組合せ論とその周辺
  • Place of Presentation: 東北大学大学院情報科学研究科
  • Year and Date: 2016-03-08
  • Invited
• [Presentation] Triply even codes constructed from distance regular graphs (2016)
  • Author(s): 別宮 耕一
  • Organizer: RIMS研究集会 有限群とその表現, 頂点作用素代数, 代数的組合せ論の研究
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2016-01-05
  • Invited
• [Presentation] 立方重偶符号の自己同型群に現れる単純群 (2015)
  • Author(s): 別宮 耕一
  • Organizer: 第27回有限群論草津セミナー
  • Place of Presentation: 草津セミナーハウス
  • Year and Date: 2015-08-02
• [Presentation] 立方重偶符号について (2015)
  • Author(s): 別宮 耕一
  • Organizer: 日本数学会東北支部会
  • Place of Presentation: 東北大学大学院情報科学研
  • Year and Date: 2015-02-14
• [Presentation] Maximal triply even codes constructed by combinatorial designs (2014)
  • Author(s): 別宮 耕一
  • Organizer: Workshop on Hadamard Matrices and Combinatorial Designs
  • Place of Presentation: 東北大学大学院情報科学研究科
  • Year and Date: 2014-10-31
• [Presentation] 組合せ構造における純粋ナッシュ均衡性 (2014)
  • Author(s): 別宮 耕一
  • Organizer: 第26回有限群論草津セミナー
  • Place of Presentation: 草津セミナーハウス
  • Year and Date: 2014-08-01 – 2014-08-04
• [Remarks] DATABASE : Triply Even Codes of Length 48
  • URL: http://www.st.hirosaki-u.ac.jp/~betsumi/triply-even/