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arXiv · 1405.5421

New quantum MDS codes derived from constacyclic codes

Liqi Wang·Shixin Zhu
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Abstract

Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. It is very hard to construct quantum MDS codes with relatively large minimum distance. In this paper, based on classical constacyclic codes, we construct two classes of quantum MDS codes with parameters $$[[λ(q-1),λ(q-1)-2d+2,d]]_q$$ where $2\leq d\leq (q+1)/2+λ-1$, and $q+1=λr$ with $r$ even, and $$[[λ(q-1),λ(q-1)-2d+2,d]]_q$$ where $2\leq d\leq (q+1)/2+λ/2-1$, and $q+1=λr$ with $r$ odd. The quantum MDS codes exhibited here have parameters better than the ones available in the literature.

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Liqi Wang, Shixin Zhu. 2014-05-21. New quantum MDS codes derived from constacyclic codes. https://arxiv.org/abs/1405.5421

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