Skew Constacyclic Codes Over the Ring

Abstract

Skew constacyclic codes are displaying vital role in the field of coding theory. This paper is mainly focused on skew-α constacyclic codes over R = Fq + uFq + vFq + uvFq, with u 2 = v 2 = 1, uv = vu, q = 3 m , and α is an unit of R fixed by the authomorphism θ. It is briey derived as well that the Gray map of skew cyclic code of length n over R is skew quasicyclic code of length 4n over Fq of index 4. Furthermore, the decomposition of a skew α constacyclic codes over R are also determined. A complete analysis about the relationship between skew α constacyclic code and its dual is also carried out.