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arXiv:1003.3754

Quantum codes from codes over Gaussian integers with respect to the Mannheim metric

Murat Güzeltepe, Mehmet Özen

Published Mar 19, 2010• 2 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]]4+i).
DOI
10.48550/arxiv.1003.3754

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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​).
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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 $2\ensuremath{\le}d\ensuremath{\le}(q+3)/2$.