On the equivalence of codes over finite rings

被引：20

作者：

Dinh, HQ ^{[1
]}

López-Permouth, SR ^{[1
]}

机构：

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

来源：

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING | 2004年 / 15卷 / 01期

关键词：

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

D O I：

10.1007/s00200-004-0149-5

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

It is known that if a finite ring R is Frobenius then equivalences of linear codes over R are always monomial transformations. Among other results, in this paper we show that the converse of this result holds for finite local and homogeneous semilocal rings. Namely, it is shown that for every finite ring R which is a direct sum of local and homogeneous semilocal subrings, if every Hamming-weight preserving R-linear transformation of a codeC(1) onto a code C-2 is a monomial transformation then R is a Frobenius ring.

引用

页码：37 / 50

页数：14

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