Skew Constacyclic Codes over Finite Fields and Finite Chain Rings

Abstract

This paper overviews the study of skew Θ-constacyclic codes over finite fields and finite commutative chain rings. The structure of skew Θ-constacyclic codes and their duals are provided. Among other results, we also consider the Euclidean and Hermitian dual codes of skew Θ-cyclic and skew Θ-negacyclic codes over finite chain rings in general and over Fpm+uFpm in particular. Moreover, general decoding procedure for decoding skew BCH codes with designed distance and an algorithm for decoding skew BCH codes are discussed.