Cyclic codes over the ring $\mathbb{F}_p[u,v,w]/\langle u^2, v^2, w^2, uv-vu, vw-wv, uw-wu \rangle$
Information Theory
2015-09-30 v2 math.IT
Abstract
In this paper, we investigate cyclic codes over the ring , , where is a prime number. Which is a part of family of Frobenius rings. We find a unique set of generators for these codes and characterize the free cyclic codes. We also study the rank and the Hamming distance of these codes. We also constructs some good codes as the Gray images of these cyclic codes.
Keywords
Cite
@article{arxiv.1509.04221,
title = {Cyclic codes over the ring $\mathbb{F}_p[u,v,w]/\langle u^2, v^2, w^2, uv-vu, vw-wv, uw-wu \rangle$},
author = {Pramod Kumar Kewat and Sarika Kushwaha},
journal= {arXiv preprint arXiv:1509.04221},
year = {2015}
}
Comments
Rewriting of Section 4. arXiv admin note: substantial text overlap with arXiv:1508.07034, arXiv:1405.5981