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Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi

Quantum Codes from (1-2w-2uv)-Constacyclic Codes over the F_q+uF_q+vF_q+wF_q+uvF_q

Ceremnur Tetik, Abdullah Dertli

Published Mar 27, 2022• 0 citations
Publisher

Abstract

In this paper, we give construction of quantum codes over F_q from (1-2w-2uv) - constacyclic 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 (1-2w-2uv) - constacyclic codes over the F_q+uF_q+vF_q+wF_q+uvF_q.

DOI
10.18185/erzifbed.911472

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In this paper, we give construction of quantum codes over F_q from (1-2w-2uv) - constacyclic 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 (1-2w-2uv) - constacyclic codes over the F_q+uF_q+vF_q+wF_q+uvF_q.
In this article, we construct some MDS quantum error-correcting codes (QECCs) from classes of constacyclic codes over Rs= Fp+ u1Fp+ ··· + usFp, ui2= ui, uiuj= ujui= 0, for odd prime p and i, j = 1, 2,⋯, s, i ≠ j. Many QECCs with improved parameters than the existing ones in some of the earlier papers are provided. We present a set of idempotent generators of the ring Rs, and using that we define linear codes, determine all units, and study constacyclic codes over this ring. Among others, we study dual containing constacyclic codes over Rs and construct (non-binary) QECCs. An algorithm to construct QECCs from dual containing constacyclic codes over Rs is obtained that can provide many quantum codes.
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