Title: Skew cyclic codes over 𝔽_p + u𝔽_p

Authors: R. Dastbasteh; H. Mousavi; T. Abualrub; N. Aydin; J. Haghighat

Addresses: Department of Mathematics, Simon Fraser University, Vancouver, V5A 1S6, Canada ' Department of Electrical Engineering, Shiraz University of Technology, Shiraz, 71557-13876, Iran ' Department of Mathematics and Statistics, American University of Sharjah, Sharjah, 61485, UAE ' Department of Mathematics and Statistics, Kenyon College, Gambier, Ohio, 43022, USA ' Department of Electrical Engineering, Shiraz University of Technology, Shiraz, 71557-13876, Iran

Abstract: In this paper, we study skew cyclic codes with arbitrary length over the ring R = 𝔽_p + u𝔽_p where p is an odd prime and u² = 0. We characterise all skew cyclic codes of length n as left R[x;θ]-submodules of R_n = R[x;θ] / ⟨xⁿ − 1⟩. We find all generator polynomials for these codes and describe their minimal spanning sets. Moreover, an encoding algorithm is presented for skew cyclic codes over the ring R. Finally, based on the theory we developed in this paper, we provide examples of codes with good parameters over F_p with different odd primes p: In fact, example 6 in our paper is a new ternary code in the class of quasi-twisted codes. We also present several examples of optimal codes.

Keywords: skew cyclic codes; optimal codes; codes over rings.

DOI: 10.1504/IJICOT.2018.091854

International Journal of Information and Coding Theory, 2018 Vol.5 No.1, pp.81 - 99

Received: 18 Dec 2017
Accepted: 02 Feb 2018
Published online: 18 May 2018 *