Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2016; 53(6): 1617-1628

Online first article November 3, 2016      Printed November 30, 2016

https://doi.org/10.4134/BKMS.b150544

Copyright © The Korean Mathematical Society.

On quantum codes from cyclic codes over a class of nonchain rings

Mustafa Sari and Irfan Siap

Yildiz Technical University, Yildiz Technical University

Abstract

In this paper, we extend the results given in \cite{2.5} to a nonchain ring $R_p={\mathbb{F}_p} + v{\mathbb{F}_p} + \cdots + {v^{p - 1}}{\mathbb{F}_p}$, where ${v^p} = v$ and $p$ is a prime. We determine the structure of the cyclic codes of arbitrary length over the ring $R_p$ and study the structure of their duals. We classify cyclic codes containing their duals over $R_p$ by giving necessary and sufficient conditions. Further, by taking advantage of the Gray map $\pi$ defined in \cite{2.7}, we give the parameters of the quantum codes of length $pn$ over $\mathbb{F}_p$ which are obtained from cyclic codes over $R_p.$ Finally, we illustrate the results by giving some examples.

Keywords: quantum codes, cyclic codes, gray map

MSC numbers: 81P70, 94B15