Skew Constacyclic Codes over Finite Commutative Semi-Simple Rings

This paper investigates skew Θ − λ-constacyclic codes over R = F₀⊕F₁⊕⋯⊕F_k−1, where F^i′s are finite fields. The structures of skew λ-constacyclic codes over finite commutative semi-simple rings and their duals are provided. Moreover, skew λ-constacyclic codes of arbitrary length are studied under a new definition. We also show that a skew cyclic code of arbitrary length over finite commutative semi-simple rings is equivalent to either a cyclic code over R or a quasi-cyclic code over R.