Structure and performance of generalized quasi-cyclic codes

被引：34

作者：

Guneri, Cem ^{[1
]}

Ozbudak, Ferruh ^{[3
]}

Ozkaya, Buket ^{[1
]}

Sacikara, Elif ^{[1
]}

Sepasdar, Zahra ^{[4
]}

Sole, Patrick ^{[2
]}

机构：

[1] Sabanci Univ, Istanbul, Turkey

[2] Univ Paris 08, CNRS, LAGA, F-93526 St Denis, France

[3] Middle East Tech Univ, Ankara, Turkey

[4] Ferdowsi Univ Mashhad, Dept Pure Math, Mashhad, Iran

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2017年 / 47卷

关键词：

GQC codes; QC codes; LCD codes; Self-dual codes; ALGEBRAIC STRUCTURE;

D O I：

10.1016/j.ffa.2017.06.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder Theorem yields a decomposition of GQC codes into a sum of concatenated codes. This decomposition leads to a trace formula, a minimum distance bound, and to a criteria for the GQC code to be self-dual or to be linear complementary dual (LCD). Explicit long GQC codes that are LCD, but not QC, are exhibited. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：183 / 202

页数：20

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