Enumeration and construction of additive cyclic codes over Galois rings

被引：7

作者：

Cao, Yonglin ^{[1
]}

Gao, Jian ^{[2
,3
]}

Fu, Fang-Wei ^{[2
,3
]}

Cao, Yuan ^{[4
]}

机构：

[1] Shandong Univ Technol, Sch Sci, Zibo 255091, Shandong, Peoples R China

[2] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

[4] Hunan Univ, Coll Elect & Informat Engn, Changsha 410082, Hunan, Peoples R China

来源：

DISCRETE MATHEMATICS | 2015年 / 338卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Additive cyclic code; Galois ring; Linear code; Dual code; Trace inner product; Self-dual code; Quasi-cyclic code; CLASSIFICATION;

D O I：

10.1016/j.disc.2015.01.012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R = GR(p(epsilon), l) be a Galois ring of characteristic p(epsilon) and cardinality p(epsilon l), where p and l are prime integers. First, we give a canonical form decomposition for additive cyclic codes over R. This decomposition is used to construct additive cyclic codes and count the number of such codes, respectively. Then we give the trace dual code for each additive cyclic code over R from its canonical form decomposition and linear codes of length I over some extension Galois rings of Zp(epsilon). (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：922 / 937

页数：16

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