Cyclic codes over the ring $ \Z_p[u, v]/\langle u^2, v^2, uv-vu\rangle$
Information Theory
2014-06-05 v2 math.IT
Abstract
Let be a prime number. In this paper, we study cyclic codes over the ring . We find a unique set of generators for these codes. We also study the rank and the Hamming distance of these codes. We obtain all except one ternary optimal code of length 12 as the Gray image of the cyclic codes over the ring . We also characterize the -ary image of these cyclic codes under the Gray map.
Keywords
Cite
@article{arxiv.1405.5981,
title = {Cyclic codes over the ring $ \Z_p[u, v]/\langle u^2, v^2, uv-vu\rangle$},
author = {Pramod Kumar Kewat and Bappaditya Ghosh and Sukhamoy Pattanayak},
journal= {arXiv preprint arXiv:1405.5981},
year = {2014}
}
Comments
Following things included: ternary optimal code of length 12, characterization p-ary image and some minor changes