摘要：

设R为有限链环，定义从Rn到 的Gray映射 ，给出Gray映射 的一个性质。利用Gray映射的性质研究有限链环R上任意长循环码的Gray象。证明有限链环R上长为n的码C是循环码当且仅当它的Gray象 是有限域Fp上指标为pe-1长为npe-1的准循环码。

关键词: 线性码, 循环码, 准循环码, Gray映射

Abstract:

Let R be a finite chain ring, the Gray map from Rn to is defined, and a property of the Gray map is given. Based on the property of Gray map, the Gray image of a cyclic code of arbitrary length over R is studied. It is proved that a code of length n over R is a cyclic code if and only if its Gray image is a quasi-cyclic code over Fp of index pe-1 and of length npe-1.

Key words: linear code, cyclic code, quasi-cyclic code, Gray map

中图分类号: 

• TP312