A Geometric Study on the Bound for Error-Correcting Linear Codes

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540138
• 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: Osaka Prefecture University
• Principal Investigator: MARUTA Tatsuya 大阪府立大学, 理学(系)研究科(研究院), 教授 (80239152)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 線形符号 / 最適符号 / 符号の拡張 / Griesmer 限界 / 有限幾何 / 射影幾何

Outline of Final Research Achievements

A linear code over the field of q elements with length n, dimension k and minimum distance d is called an [n,k,d]q code. A fundamental research problem in coding theory is to find dq(n,k), the maximum value of d for which an [n,k,d]q code exists (this problem is equivalent to find nq(k,d), the minimum value of n for which an [n,k,d]q code exists). In this work, we have obtained several new results on the problem by constructing new codes and showing the nonexistence of some linear codes attaining the known bound using the geometric methods through projective geometry over finite fields.

Free Research Field

代数的符号理論