有限非链环F_(q)+vF_(q)上的2维斜常循环码

2-D Skew Constacyclic Codes over Finite Non-Chain Ring F_(q)+vF_(q)

令R=F_(q)+vF_(q)是一个有限非链环,其中q是一个奇素数的方幂,v^(2)=v.文章利用二元斜多项式环R[x,y;ρ,θ]来研究环R上的2维斜常循环码的代数结构和相关性质,其中ρ和θ是环R上的两个自同构映射.基于中国剩余定理,文章确定了环R上2维(α_(1)+β_(1)v,α_(2)+β_(2)v)-斜常循环码的生成元结构并且考虑了它们的Gray象,其中α_(1)+β_(1)v和α_(2)+β_(2)v都是环R上的可逆元.此外,文章研究了环R上2维(α_(1)+β_(1)v,α_(2)+β_(2)v)-斜常循环码的对偶码并且确定了对偶码子码的生成元结构.

Let R= F_(q)+vF_(q) be a finite non-chain ring,where q is an odd prime power and v^(2)= v.In this paper,we study the algebraic structure and related properties of 2-D skew constacyclic codes over R using the bivariate skew polynomial ring R[x,y;ρ,θ],where ρ and θ are two automorphisms of R.We determine the structure of generators of 2-D skew(α_(1)+β_(1)v,α_(2)+β_(2)v)-constacyclic codes by Chinese Reminder Theorem and consider their Gray images,where α_(1)+β_(1)v and α_(2)+/β_(2)v are units of R.Moreover,we study the dual codes of 2-D skew(α_(1)+β_(1)v,α_(2)+β_(2)v)-constacyclic codes over R and determine the structure of generators of subcodes of the dual codes.