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 s ℓ k and their duals over a finite field F q , where α , β , γ are non zero elements of F q . We give necessary and sufficient conditions for a three-dimensional (α , β , γ) -constacyclic code to be self-dual. [ABSTRACT FROM AUTHOR]