摘要
环R=Z4+uZ4+u2 Z4既不是有限链环也不是主理想环,其中u3=0。文章研究了环Z4+uZ4+u2 Z4上任意长度的循环码,确定了R上任意长度n的循环码的结构,定义了R到Z34的一个Gray映射,证明了R上长为n的循环码的Gray像是Z4上长为3n、指数为3的准循环码。
The ring R=Z4＋uZ4＋u2Z4 is neither a finite ring nor a principle ideal ring,, where u3 =0. In this paper, cyclic codes over R of an arbitrary length are studied. The structure of cyclic codes over R of length n is determined. A Gray map from R to Z43 is defined. It is proved that the Gray map of a cyclic code over R of length n is a quasi-cyclic code of length 3n and index 3 over Z4.
出处
《合肥工业大学学报（自然科学版）》
CAS
CSCD
北大核心
2016年第10期1432-1436,1440,共6页
Journal of Hefei University of Technology：Natural Science
基金
国家自然科学基金资助项目(11201107
11401154)
关键词
循环码
环同态
GRAY映射
准循环码
cyclic code
ring homomorphism
Gray map
quasi-cyclic code
