Some constructions of linearly optimal group codes

被引：3

作者：

Couselo, Elena ^{[1
]}

Gonzalez, Santos ^{[1
]}

Markov, Victor ^{[2
]}

Martinez, Consuelo ^{[1
]}

Nechaev, Alexander ^{[2
]}

机构：

[1] Univ Oviedo, Dept Math, Oviedo, Spain

[2] Moscow MV Lomonosov State Univ, Ctr New Informat Technol, Moscow, Russia

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2010年 / 433卷 / 02期

关键词：

Group code; Linearly optimal code; Reed-Solomon code; Group ring;

D O I：

10.1016/j.laa.2010.03.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We continue here the research on (quasi)group codes over (quasi)group rings. We give some constructions of [n, n - 3, 3](q)- codes over F-q for n = 2q and n = 3q. These codes are linearly optimal, i.e. have maximal dimension among linear codes having a given length and distance. Although codes with such parameters are known, our main results state that we can construct such codes as (left) group codes. In the paper we use a construction of Reed-Solomon codes as ideals of the group ring F(q)G where G is an elementary abelian group of order q. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：356 / 364

页数：9

共 10 条

[1]

ANDRIES EB, 1998, HDB CODING THEORY, P295

[2]

[Anonymous], INFORM CODIERUNGSTHE

[3]

[Anonymous], DISCRETE MATH APPL

[4]

EVANS SR, 1993, NOTES COMPUT SCI, V673, P279

[5]

EVANS SR, 1993, NOTES PURE APPL MATH, V141, P183

[6]

EVANS SR, 1995, APPL ALGEBR ENG COMM, V6, P191

[7]

Landrock P., 1992, Designs, Codes and Cryptography, V2, P273, DOI 10.1007/BF00141972

[8]

Lang, 1965, Algebra

[9]

MacWilliams F. J., 1988, THEORY ERROR CORRECT

[10]

Niederreiter H., 1983, FINITE FIELDS

← 1 →