Title: F₃R-skew cyclic codes

Authors: Amit Sharma; Maheshanand Bhaintwal

Addresses: Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India ' Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India

Abstract: In this paper, a new class of skew-cyclic codes, termed as F₃R-skew cyclic codes, is defined, where R denotes the ring F₃ + uF₃, u² = u. These codes are of length α + β and are submodules of the R-module F₃^αR^β. We study some structural properties of skew cyclic codes over R and F₃R-skew cyclic codes. The generator polynomials of these codes are studied. Some examples are given to illustrate the results. An optimal ternary code is obtained as the Gray image of an F₃R-skew cyclic code.

Keywords: F₃R-skew cyclic codes; Gray map; non-commutative rings; skew cyclic codes; generator polynomials.

DOI: 10.1504/IJICOT.2016.076967

International Journal of Information and Coding Theory, 2016 Vol.3 No.3, pp.234 - 251

Received: 24 Feb 2016
Accepted: 27 Feb 2016
Published online: 08 Jun 2016 *

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