Two Dimensional $\left(\alpha ,\beta \right)$-Constacyclic Codes of arbitrary length over a Finite Field

Abstract

In this paper we characterize the algebraic structure of two-dimensional $(\alpha ,\beta )$-constacyclic codes of arbitrary length $s.\ell$ and of their duals. For $\alpha ,\beta \in \{1,-1\}$, we give necessary and sufficient conditions for a two-dimensional $(\alpha ,\beta )$-constacyclic code to be self-dual. We also show that a two-dimensional $(\alpha ,1)$-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 $(\alpha ,\beta )$-constacyclic codes.

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