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Quantum Codes From Codes Over Gaussıan Integers Wıth Respect To The Mannheım Metrıc

Sakarya Üniversitesi/Eğitim Fakültesi/Bilgisayar Ve Öğretim Teknolojileri Eğitimi Bölümü, Murat Güzeltepe

Published Jan 1, 2012• 0 citations
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Abstract

In this paper, some nonbinary quantum codes using classical codes over Gaussian integers are obtained. Also, some of our quantum codes are better than or comparable with those known before, (for instance [8, 2, 5]).

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In this paper, some nonbinary quantum codes using classical codes over Gaussian integers are obtained. Also, some of our quantum codes are better than or comparable with those known before, (for instance [[8,2,5]]4+i[[8,2,5]]_{4+i}[[8,2,5]]4+i​).
Most of quantum codes have been constructed by using classical linear codes over finite field. However, little is known about the construction of quantum codes via group character codes. In this work, we present the constructions of nonbinary quantum and asymmetric quantum codes based on group character codes, and give explicit parameters for infinite families of nonbinary quantum codes and asymmetric quantum codes. Furthermore, we present families of optimal quantum codes which derived from group character codes.
In this paper, we construct families of nonbinary quantum codes from classical negacyclic codes. The BCH bound for negacyclic codes is applied to determine the dimension and distance of these quantum codes. The parameters of these quantum codes are good compared with the ones available in the literature. We also construct a family of quantum maximum-distance-separable codes with parameters ${[[q+1,q\ensuremath{-}2d+3,d]]}_{q}$, where $q\ensuremath{\equiv}1\phantom{\rule{0.28em}{0ex}}\mathrm{mod}\phantom{\rule{0.28em}{0ex}}4$ and $2\ensuremath{\le}d\ensuremath{\le}(q+3)/2$.