Optimal Linear Codes Problem

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20540129
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Osaka Prefecture University
• Principal Investigator: MARUTA Tatsuya Osaka Prefecture University, 大学院・理学系研究科, 教授 (80239152)
• Project Period (FY): 2008 – 2011
• Keywords: Griesmer限界 / 射影幾何 / 最適符号 / 符号の拡張 / 線形符号 / 誤り訂正

Research Abstract

q元体上の長さn,次元k,最小距離dの線形符号([n,k,d]_q符号)が存在する限界(具体的にはnの最小値n_q(k,d))を決定する最適線形符号問題に関する研究に取り組む。

Research Products

• [Journal Article] On optimal linear codes over F_8 (2011)
  • Author(s): R.Kanazawa, T.Maruta
  • Journal Title: Electronic J.Combinatorics 18 Pages: #P34(27)
  • Peer Reviewed
• [Journal Article] An extension theorem for [n, k, d]_q codes with gcd(d, q)=2 (2010)
  • Author(s): Y.Yoshida, T.Maruta
  • Journal Title: Australasian J.Combinatorics 48 Pages: 117-131
  • Peer Reviewed
• [Journal Article] A An improvement to the achievement of the Griesmer bound (2010)
  • Author(s): N.Hamada, T.Maruta
  • Journal Title: Serdica Journal of Computing 4 Pages: 301-320
  • Peer Reviewed
• [Journal Article] A new extension theorem for 3-weight modulo q linear codes over F_q (2009)
  • Author(s): E.J.Cheon, T.Maruta
  • Journal Title: Designs, Codes and Cryptography 52 Pages: 171-183
  • Peer Reviewed
• [Journal Article] Ternary linear codes and quadrics (2009)
  • Author(s): Y.Yoshida, T.Maruta
  • Journal Title: Electronic J.Combinatorics 16 Pages: #R9(21)
  • Peer Reviewed
• [Presentation] New ternary linear codes of dimension 6 (2010)
  • Author(s): T.Maruta, Y.Oya
  • Organizer: 12th International Workshop on Algebraic and Combinatorial Coding Theory
  • Place of Presentation: Novosibirsk(ロシア)
  • Year and Date: 2010-09-06
• [Presentation] Extension theorems for linear codes over finite fields (2010)
  • Author(s): T.Maruta
  • Organizer: Combinatorics 2010
  • Place of Presentation: Verbania(イタリア)招待講演
  • Year and Date: 2010-06-29
• [Presentation] An improvement of Landjev-Rousseva's extension theorem for linear codes (2009)
  • Author(s): T.Maruta
  • Organizer: 33rd Australasian Conference on Combinatorial Mathematics and Combinatorial Computing
  • Place of Presentation: Newcastle(オーストラリア)
  • Year and Date: 2009-12-08
• [Presentation] On the nonexistence of some q-ary linear codes meeting the Griesmer bound (2009)
  • Author(s): T.Maruta
  • Organizer: 9th International Conference on Finite Fields and Applications
  • Place of Presentation: Dublin(アイルランド)
  • Year and Date: 2009-07-13
• [Presentation] On the classification of (n, r)- arcs in PG (2, q) (2008)
  • Author(s): T.Maruta
  • Organizer: Fourth Int.Conference on Combinatorial Mathematics and Combinatorial Computing
  • Place of Presentation: Auckland(ニュージーランド)
  • Year and Date: 2008-12-18