环Zk上中国积循环码

数学物理学报 ›› 2012, Vol. 32 ›› Issue (4): 720-728.

环Z_k上中国积循环码

唐永生^1,2, 朱士信¹, 施敏加³

1.合肥工业大学数学学院合肥 |230009|2.合肥师范学院数学系合肥 230601|3.安徽大学数学系合肥 |230039

收稿日期:2010-08-05 修回日期:2011-11-30 出版日期:2012-08-25 发布日期:2012-08-25
基金资助:
国家自然科学基金(60973125, 11126174)、安徽省高校优秀青年人才基金重点项目(2012SQRL020ZD)、合肥师范学院一般项目(2012kj10)和安徽省高校省级自然科学研究项目(KJ2010B171)资助

Chinese Product of Cyclic Codes over Z_k

TANG Yong-Sheng^1,2, ZHU Shi-Xin¹, SHI Min-Jia³

1.School of Mathematics, Hefei University of Technology, Hefei 230009|
2.Department of Mathematics, Hefei Normal University, Hefei 230601;
3.Department of Mathematics, Anhui University, Hefei 230039

Received:2010-08-05 Revised:2011-11-30 Online:2012-08-25 Published:2012-08-25
Supported by:
国家自然科学基金(60973125, 11126174)、安徽省高校优秀青年人才基金重点项目(2012SQRL020ZD)、合肥师范学院一般项目(2012kj10)和安徽省高校省级自然科学研究项目(KJ2010B171)资助

摘要/Abstract

摘要：

利用中国剩余定理研究了环Z_k上循环码及其对偶码, 其中k=(∏_i=1^sp_i)^m, p_i表示不同的素数, m 是一个正整数, 并且p_i不能整除码长n, 给出了一个非平凡循环自对偶码存在的充要条件, 得到了中国积循环码最小距离的上界, 并且确定了中国积循环码的秩和最小生成集.

关键词: 中国剩余定理, 循环码, 生成集

Abstract:

In this paper, we describe the Chinese Remainder Theorem for studying cyclic and dual cyclic codes over the ring Z_k, where k=(∏_i=1^sp_i)^m, the p_iare distinct primes and m is a positive integer, also with the condition that the code length n cannot be divided by p_i. A necessary and sufficient condition for the existence of nontrivial cyclic self-dual codes is given. The upper bound of minimum distance of such cyclic codes is also obtained. Furthermore, we determine the minimal generator set and the rank of such cyclic codes.

Key words: The Chinese Remainder Theorem, Cyclic codes, Generator set

中图分类号:

94B05

唐永生, 朱士信, 施敏加. 环Z_k上中国积循环码[J]. 数学物理学报, 2012, 32(4): 720-728.

TANG Yong-Sheng, ZHU Shi-Xin, SHI Min-Jia. Chinese Product of Cyclic Codes over Z_k[J]. Acta mathematica scientia,Series A, 2012, 32(4): 720-728.

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