环R+vR上的斜常循环码

Skew constacyclic codes over rings R+vR

本文主要研究了环ℜ=R+vR(v2=1)上斜常循环码,其中R是有限链环。利用环ℜ的直和分解,我们证明了环ℜ上长度为n的线性码C是斜常循环码的充分必要条件:C1是环ℜ上长度为n的斜循环码,且C2是环ℜ上长度为n的斜负循环码。同时,本文也讨论了斜常循环码的对偶码的生成多项式。

In this paper,we mainly discuss the constacyclic codes on ringsℜ=R+vR(v2=1),where R is a finite chain ring.Through the direct sum decomposition of the ringℜ,it is proved that a linear code C of length n over the ringℜis the skew constatcyclic code if and only if C1 is skew cyclic codes,and C2 is skew negative cyclic codes over the ring.Furthermore,the generating polynomial of their dual codes is discussed.