Authors: Habibul Islam; Om Prakash
Addresses: Department of Mathematics, Indian Institute of Technology Patna, Patna-801 106, India ' Department of Mathematics, Indian Institute of Technology Patna, Patna-801 106, India
Abstract: In this note, we study skew cyclic and skew constacyclic codes over the ring R = Fq + uFq + vFq + uvFq where q = pm; p is an odd prime, u2 = u, v2 = v, uv = vu. We show that Gray images of a skew cyclic and skew-constacyclic codes of length n over R are skew quasi-cyclic codes of length 4n over Fq of index 4. Also, it is shown that skew α-constacyclic codes are either equivalent to α-constacyclic codes or α-quasi-twisted codes over R. Further, structural properties, specially, generating polynomials and idempotent generators for skew cyclic and skew constacyclic codes are determined by decomposition method.
Keywords: skew polynomial ring; skew cyclic code; skew quasi-cyclic code; skew constacyclic code; Gray map; generating polynomial; idempotent generator.
International Journal of Information and Coding Theory, 2018 Vol.5 No.2, pp.101 - 116
Received: 10 Jan 2018
Accepted: 04 Mar 2018
Published online: 24 Sep 2018 *