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http://dx.doi.org/10.4134/BKMS.b150544

ON QUANTUM CODES FROM CYCLIC CODES OVER A CLASS OF NONCHAIN RINGS  

Sari, Mustafa (Department of Mathematics Faculty of Art and Sciences Yildiz Technical University)
Siap, Irfan (Department of Mathematics Faculty of Art and Sciences Yildiz Technical University)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.6, 2016 , pp. 1617-1628 More about this Journal
Abstract
In this paper, we extend the results given in [3] 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 [4], 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;
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