On the equivalence of codes over rings and modules

被引：26

作者：

Dinh, HQ ^{[1
]}

López-Permouth, SR ^{[1
]}

机构：

[1] Ohio Univ, Dept Math, Athens, OH 45701 USA

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2004年 / 10卷 / 04期

关键词：

equivalence of codes; codes over finite rings; codes over finite modules; finite Frobenius rings;

D O I：

10.1016/j.ffa.2004.01.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In light of the result by Wood that codes over every finite Frobenius ring satisfy a version of the MacWilliams equivalence theorem, a proof for the converse is considered. A strategy is proposed that would reduce the question to problems dealing only with matrices over finite fields. Using this strategy, it is shown, among other things, that any left MacWilliams basic ring is Frobenius. The results and techniques in the paper also apply to related problems dealing with codes over modules. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：615 / 625

页数：11

共 17 条

[1] ELEMENTARY PROOF OF MACWILLIAMS THEOREM ON EQUIVALENCE OF CODES [J].