Title: Skew cyclic and skew (α₁ + uα₂ + vα₃ + uvα₄)-constacyclic codes over F_q + uF_q + vF_q + uvF_q

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 = F_q + uF_q + vF_q + uvF_q where q = p^m; 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 F_q 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.

DOI: 10.1504/IJICOT.2018.095008

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: 28 Sep 2018 *

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