Cyclic codes over the ring $ \Z_p[u, v]/\langle u^2, v^2, uv-vu\rangle$

Autor:	Kewat, Pramod Kumar, Ghosh, Bappaditya, Pattanayak, Sukhamoy
Rok vydání:	2014
Předmět:	Computer Science - Information Theory
Druh dokumentu:	Working Paper
Popis:	Let $p$ be a prime number. In this paper, we study cyclic codes over the ring $ \Z_p[u, v]/\langle u^2, v^2, uv-vu\rangle$. 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 $ \Z_p[u, v]/\langle u^2, v^2, uv-vu\rangle$. We also characterize the $p$-ary image of these cyclic codes under the Gray map. Comment: Following things included: ternary optimal code of length 12, characterization p-ary image and some minor changes
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1405.5981 Zobrazit plný text záznamu View this record from Arxiv