环Fq+uFq+u2Fq上任意长度的负循环码

doi:10.3969/j.issn.0253-2778.2014.12.005

中国科学技术大学学报 ›› 2014, Vol. 44 ›› Issue (12): 991-995.DOI: 10.3969/j.issn.0253-2778.2014.12.005

• 论著 • 上一篇

环Fq+uFq+u2Fq上任意长度的负循环码

黄磊，朱士信

合肥工业大学数学学院，安徽合肥 230009

收稿日期:2013-12-25 修回日期:2014-04-10 接受日期:2014-04-10 出版日期:2014-04-10 发布日期:2014-04-10
通讯作者: 朱士信
作者简介:黄磊，男，1989年生，硕士. 研究方向：代数编码与密码. E-mail：1306926448@qq.com
基金资助:
国家自然科学基金(61370089)资助.

Negacyclic codes of arbitrary lengths over ring Fq+uFq+u2Fq

HUANG Lei, ZHU Shixin

School of Mathematics, Hefei University of Technology, Hefei 230009, China

Received:2013-12-25 Revised:2014-04-10 Accepted:2014-04-10 Online:2014-04-10 Published:2014-04-10

摘要/Abstract

摘要： 根据环Fq+uFq上负循环码的结构，研究了环Fq+uFq+u2Fq上任意长度的负循环码.利用环同态，给出了环Fq+uFq+u2Fq上长度为n的负循环码的结构，并研究了这些负循环码的对偶码，同时研究了该环上自对偶负循环码.结果表明环Fq+uFq+u2Fq上自对偶负循环码存在当且仅当p=2.

关键词: 负循环码, 环同态, 对偶码, 自对偶码

Abstract: According to the structure of negacyclic codes over ring Fq+uFq, the negacyclic codes of arbitrary lengths over ring Fq+uFq+u2Fq were studied. Bying ring homomorphism, the structure of negacyclic codes over ring Fq+uFq+u2Fq of length n were given, the dual codes of these negacyclic codes were studied, and the self-dual negacyclic codes over the ring were also studied. The results show that self-dual negacyclic codes over ring Fq+uFq+u2Fq exist if and only if p=2.

Key words: negacyclic codes, ring homomorphism, dual codes, self-dual codes

中图分类号:

TN911.22

黄磊，朱士信. 环Fq+uFq+u2Fq上任意长度的负循环码[J]. 中国科学技术大学学报, 2014, 44(12): 991-995.

HUANG Lei, ZHU Shixin. Negacyclic codes of arbitrary lengths over ring Fq+uFq+u2Fq[J]. Journal of University of Science and Technology of China, 2014, 44(12): 991-995.

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环Fq+uFq+u2Fq上任意长度的负循环码

Negacyclic codes of arbitrary lengths over ring Fq+uFq+u2Fq

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