有限域上任意长度的二维的$\left( α,β\right) $ -常循环码
Two Dimensional $\left( α,β\right) $-Constacyclic Codes of arbitrary length over a Finite Field
摘要：
本文刻画了任意长度的二维$(α,β)$ -常循环码$s.\ell$的代数结构和它们的代数结构。对于$α,β\in \{1,-1\}$，给出了二维$(α,β)$ -常循环码是自对偶码的充要条件.我们还证明了长度为$n=s.\ell$的二维$(α,1 )$ -常循环码$\mathcal{C}$不可能是自对偶的，如果$\gcd(s,q)= 1$ .最后给出了二维$(α,β)$ -常循环码的自对偶码、等对偶码、MDS码和准扭码的例子。
英文摘要：
In this paper we characterize the algebraic structure of two-dimensional $(α,β)$-constacyclic codes of arbitrary length $s.\ell$ and of their duals. For $α,β\in \{1,-1\}$, we give necessary and sufficient conditions for a two-dimensional $(α,β)$-constacyclic code to be self-dual. We also show that a two-dimensional $(α,1 )$-constacyclic code $\mathcal{C}$ of length $n=s.\ell$ can not be self-dual if $\gcd(s,q)= 1$. Finally, we give some examples of self-dual, isodual, MDS and quasi-twisted codes corresponding to two-dimensional $(α,β)$-constacyclic codes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
