A class of skew cyclic codes and application in quantum codes construction
A class of skew cyclic codes and application in quantum codes construction
Source title:
Discrete Mathematics, 344(2): 112189,
2021
(ISI)
Academic year of acceptance:
2020-2021
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 , 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
. 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
. It is observed that some quantum codes we constructed are MDS quantum codes.