A class of skew cyclic codes and application in quantum codes construction

Abstract

Let p be an odd prime, and k an integer such that k∣(p−1). This paper studies quantum codes from skew cyclic codes over the ring R=Fq[u]〈uk+1−u〉, where q is a power of the prime p. We construct a set of orthogonal idempotents of the ring R and using the set, skew cyclic codes over the ring R are decomposed as direct sum of skew cyclic codes over Fq. We obtain a necessary and sufficient condition for a skew cyclic code to contain its dual. As an application, we construct quantum codes from skew cyclic codes over Fq. It is observed that some quantum codes we constructed are MDS quantum codes.