Multi-dimensional Constacyclic Codes of Arbitrary Length over Finite Fields

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 (α, β, γ)constacyclic codes of arbitrary length slk and their duals over a finite field Fq, where α, β, γ are non zero elements of Fq. We give necessary and sufficient conditions for a three-dimensional (α, β, γ)constacyclic code to be self-dual. MSC : 94B15, 94B05, 11T71.