F_2+uF_2和Z_4上循环码的Gray象  

Gray images of cyclic codes over F_2+uF_2 and Z_4

作　　者：梁华[1] 

机构地区：[1]淮阴师范学院数学科学学院,江苏淮安223300

出　　处：《计算机工程与应用》2010年第20期84-85,共2页Computer Engineering and Applications

基　　金：国家自然科学基金No.60971123;教育部科学技术研究重点项目No.208045;东南大学移动通信国家重点实验室开放课题(No.W200819);江苏省自然科学基金No.BK2008208~~

摘　　要：利用Gray映射Φ的性质,研究了环F2+uF2和Z4上的任意长循环码。证明了环F2+uF2上任意长码是循环码当且仅当它的Gray象是域F2上的准循环码,得到了Z4上任意长码是循环码的一个充分必要条件。特别的,环F2+uF2上长为n的线性循环码的Gray象是域F2上指标为2长为2n的线性准循环码,环Z4上长为n的线性循环码的Gray象是域F2上指标为2长为2n的准循环码。Based on the property of Gray mapΦ,cyclic codes over F2＋uF2 and Z4 are studied.It is proved that a code of arbitrary length over F2＋uF2 is a cyclic code if and only if its Gray image is a quasi-cyclic code over F2 ,and a necessary and sufficient condition for a code of arbitrary length over Z4 to be a cyclic code is obtained.In particular,the Gray image of a linear cyclic code of length n over F2＋uF2 is a linear quasi-cyclic code of index 2 and length 2n over F2 ,and the Gray image of a linear cyclic code of length n over Z4 is a quasi-cyclic code of index 2 and length 2n over F2 .

关 键 词：线性码 循环码 准循环码 GRAY映射 

分 类 号：TN911.22[电子电信—通信与信息系统]