Some Results on Cyclic Codes Over F2 + vF2

被引：72

作者：

Zhu, Shixin ^{[1
,2
]}

Wang, Yu ^{[3
]}

Shi, Minjia ^{[4
]}

机构：

[1] Hefei Univ Technol, Sch Math, Hefei 230009, Anhui, Peoples R China

[2] Southeast Univ, Natl Mobile Commun Res Lab, Nanjing 210096, Peoples R China

[3] Hefei Univ, Dept Math & Phys, Hefei 230061, Anhui, Peoples R China

[4] Anhui Univ, Sch Math Sci, Hefei 230601, Anhui, Peoples R China

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2010年 / 56卷 / 04期

关键词：

Cyclic code; gray map; generator matrix; idempotent; SELF-DUAL CODES; F(2)+UF(2); RINGS;

D O I：

10.1109/TIT.2010.2040896

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we investigate the structure and properties of cyclic codes over the ring F(2) + vF(2). We first study the relationship between cyclic codes over F(2) + vF(2) and binary cyclic codes. Then we prove that cyclic codes over the ring are principally generated, and give the generator polynomial of cyclic codes over the ring. Finally, we obtain the unique idempotent generators for cyclic codes of odd length and determine the number of cyclic codes for a given length n over F(2) + vF(2).

引用

页码：1680 / 1684

页数：5

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