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Journal of Science and Arts

QUANTUM CODES FROM CYCLIC CODES OVER THE F_q+uF_q+vF_q+wF_q+uvF_q

Ceremnur Tetik, Abdullah Dertli

Published Sep 30, 2021• 0 citations
Publisher

Abstract

In this paper, we give construction of quantum codes over F_q from cyclic codes over the F_q+uF_q+vF_q+wF_q+uvF_q, where u^2=u,v^2=v,w^2=w,uv=vu,uw=wu=vw=wv=0, q=p^m and p is an odd prime. We determine the parameters of quantum error correcting codes which constructed from cyclic codes over the F_q+uF_q+vF_q+wF_q+uvF_q. Finally, we give some examples of quantum codes.

DOI
10.46939/j.sci.arts-21.3-a01

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In this paper, we give construction of quantum codes over F_q from cyclic codes over the F_q+uF_q+vF_q+wF_q+uvF_q, where u^2=u,v^2=v,w^2=w,uv=vu,uw=wu=vw=wv=0, q=p^m and p is an odd prime. We determine the parameters of quantum error correcting codes which constructed from cyclic codes over the F_q+uF_q+vF_q+wF_q+uvF_q. Finally, we give some examples of quantum codes.
QUANTUM CODES FROM CYCLIC CODES OVER Fq+uFq+vFq\mathbb{F}_{q}+u \mathbb{F}_{q}+v \mathbb{F}_{q}Fq​+uFq​+vFq​
In this paper, we investigate the method of constructing quantum codes from cyclic codes over the ring R=Fq+uFq+vFqR= \mathbb{F}_{q}+u \mathbb{F}_{q}+v \mathbb{F}_{q}R=Fq​+uFq​+vFq​ (u2=u, v2=v, uv=vu=0). By means of the generator polynomials and some decomposition of cyclic codes and their dual over R, we give a necessary and sufficient condition of the cyclic codes over R to be construct the quantum codes. Also as an application, we obtain new non binary quantum codes from those classes of cyclic codes.