环R+uR+vR+uvR上的斜常循环码

Skew Constacyclic Codes over Rings R + uR + vR + uvR

有限连环上的斜常循环码已经得到广泛研究,本文主要讨论环?=R+uR+vR+uvR (u^2=-u,v^2=-v,uv=vu)上的斜常循环码,其中R为有限链环。通过环?的直和分解证明了环?上长为n的线性码C是斜常循环码的充分必要条件是C_1、C_4是R上的长为n的斜循环码,C_2、C_3是R上长为n的斜负循环码。进一步地,分别讨论了斜常循环码的生成矩阵与它的对偶码的生成多项式表达形式。

Skew constacyclic codes over finite links have been extensively studied.In this paper,we mainly discuss the constacyclic cyclic codes on rings R=R+u R+vR+uvR(u2=-u,v2=-v,uv=vu),where R is a finite chain ring.Through the direct sum decomposition of the rings R,it is proved that a linear code C of length n over the ring R is the skew constantcyclic code if and only if C1,C4 are skewcyclic codes and C2,C3 are skew negative cyclic codes over the ring.Furthermore,the generating matrix of skew constacyclic codes and the generating polynomial expression of their dual codes are discussed,respectively.