Multi-dimensional Constacyclic Codes of Arbitrary Length over Finite Fields

Abstract

Multi-dimensional cyclic code is a natural generalization of cyclic code. In an earlier paper we explored two-dimensional constacyclic codes over finite fields. Following the same technique, here we characterize the algebraic structure of multi-dimensional constacyclic codes, in particular three-dimensional $(\alpha ,\beta ,\gamma )$- constacyclic codes of arbitrary length $s\ell k$ and their duals over a finite field ${\mathbb{F}}_q$, where $\alpha ,\beta ,\gamma$ are non zero elements of ${\mathbb{F}}_q$. We give necessary and sufficient conditions for a three-dimensional $(\alpha ,\beta ,\gamma )$- constacyclic code to be self-dual.

21 pages. arXiv admin note: text overlap with arXiv:2007.14921