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

Abstract

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 = F q [ u ] 〈 u k + 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 F q . 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 F q . It is observed that some quantum codes we constructed are MDS quantum codes.