A circulant approach to skew-constacyclic codes

We introduce a type of skew-generalized circulant matrices that captures the structure of a skew-polynomial ring F[x;θ]F[x;θ] modulo the left ideal generated by a polynomial of the form xn−axn−a. This allows us to develop an approach to skew-constacyclic codes based on skew-generalized circulants. Properties of these circulants are derived, and in particular it is shown that for the code-relevant case the transpose of a skew-generalized circulant is a skew-generalized circulant again. This recovers the well-known result that the dual of a skew-constacyclic code is a skew-constacyclic code again. Special attention is paid to the case where xn−axn−a is central.