Title: A study of cyclic and constacyclic codes over Z₄ + uZ₄ + vZ₄

Authors: Habibul Islam; Om Prakash

Addresses: Department of Mathematics, Indian Institute of Technology Patna, Patna – 801106, India ' Department of Mathematics, Indian Institute of Technology Patna, Patna – 801106, India

Abstract: In this paper, we study some properties of cyclic and constacyclic codes over the ring R = Z₄ + uZ₄ + vZ₄ where u² = uv = vu = 0. The generator polynomials and minimal spanning set for cyclic codes over R are determined. Further, (1 + 2u) - constacyclic codes are considered and find the cyclic, quasi-cyclic and permutation equivalent to a QC code over Z₄ as the Gray images of (1 + 2u) - constacyclic codes over R.

Keywords: cyclic code; minimal spanning set; constacyclic code; quasi-cyclic code; Gray map.

DOI: 10.1504/IJICOT.2018.095017

International Journal of Information and Coding Theory, 2018 Vol.5 No.2, pp.155 - 168

Received: 24 May 2018
Accepted: 17 Jul 2018
Published online: 28 Sep 2018 *

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