Z_pZ_p[u]-加性循环码  

Z_pZ_p[u]-Additive Cyclic Codes

作　　者：卢振亮[1] 

机构地区：[1]合肥工业大学数学学院,合肥230009

出　　处：《大学数学》2017年第4期11-17,共7页College Mathematics

基　　金：国家自然科学基金(61370089);安徽省自然科学基金(1508085SQA198)

摘　　要：该文研究了Z_pZ_p[u]-加性循环码,其中p是素数,u^2=0.文中证明了(1-u)-加性常循环码与加性循环码同构,构造了Z_pZ_p[u]到Z_p^(α+pβ)的Gray映射,并证明了(1-u)-加性常循环码的Gray象是一个广义的准循环码.此外研究了Z_pZ_p[u]-加性循环码的结构,给出了Z_pZ_p[u]-加性循环码的最小生成集.Additive cyclic codes over Zp Zp[u] are discussed, where p is a prime and u^2 = 0. It is proved that （1- u） -additive constacyclic codes is isomorphic to additive cyclic codes. A new Gray map from ZpZp[u] to Zp^α＋pβ is defined, and it is proved that the Gray image of a （1- u） -additive constacyclic code is a generalized quasi-cyclic code. Additionally, the structure of Zp Zp[u] -additive cyclic codes is obtained and their minimal spanning sets are also given.

关 键 词：加性循环码 ZpZp[u]-加性循环码 Gray象 最小生成集 

分 类 号：O157.4[理学—数学]