Research On A Class Of Constacyclic Codes Over Finite Ring

Currently,the finite rings over finite fields is the focus of coding theory.In particular,finite chain rings is widely studied because of its good structure and property.The paper focuses on some of the properties of a class of constacyclic code in finite ringR=F2+u2F2+……+u7F2.The details are given as follows:1.firstly,a new Gray map is defined from R=F2+uF2+u2F2+……+u7F2to F28.A linear(1+u+u2+u3+u4+u5+u6+u7)cyclic code is studied.It show that the Gray image of a linear(1+u+u2+u3+u4+u5+u6+u7)cyclic code of length n over R is a distance-invariant linear cyclic code of lengfh8n over F2.if n is odd length,obtained the generator polynomial of the Gray image.2. What’s more,Lee weight distribution of linear codes over R is defined.some weight enumerators is defined,MacWilliams identity between linear codes and their dual over the ring is considered.3.2Furthermore,we discussed self-dual codes in this ring,a necessary and sufficient condition for the existence of the self-dual codes of this ring is proved.4. Finally, those properties extended to the general ring F2+uF2+u2F2+……+uaF2.This aspect makes the study a step better.it provides a wealth of resources to construct good codes.