Constacyclic and cyclic codes over finite chain rings  

作　　者：QIAN Jian-fa MA Wen-ping 

机构地区：[1]National Key Laboratory of ISN, Xidian University, Xi' an 710071, China

出　　处：《The Journal of China Universities of Posts and Telecommunications》2009年第3期122-125,共4页中国邮电高校学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(60773002,60672119 and 60873144);the Program for New Century Excellent Talents in University,the Scientific Research Foundation for the Returned Overseas Chinese Scholars,the Hi-Tech Research and Development Program of China(2007AA01Z472)

摘　　要：The problem of Gray image of constacyclic code over finite chain ring is studied. A Gray map between codes over a finite chain ring and a finite field is defined. The Gray image of a linear constacyclic code over the finite chain ring is proved to be a distance invariant quasi-cyclic code over the finite field. It is shown that every code over the finite field, which is the Gray image of a cyclic code over the finite chain ring, is equivalent to a quasi-cyclic code.The problem of Gray image of constacyclic code over finite chain ring is studied. A Gray map between codes over a finite chain ring and a finite field is defined. The Gray image of a linear constacyclic code over the finite chain ring is proved to be a distance invariant quasi-cyclic code over the finite field. It is shown that every code over the finite field, which is the Gray image of a cyclic code over the finite chain ring, is equivalent to a quasi-cyclic code.

关 键 词：constacyclic code Gray map quasi-cyclic code cyclic code 

分 类 号：TN919.31[电子电信—通信与信息系统] O153.3[电子电信—信息与通信工程]