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:
梁华, 唐元生. 有限链环上循环码的研究[J]. 计算机工程, 2010, 36(24): 287-288.
LIANG Hua, TANG Yuan-Sheng. Research of Cyclic Codes over Finite Chain Rings[J]. Computer Engineering, 2010, 36(24): 287-288.