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Quantum Information Processing

01-03-2015

New quantum MDS codes derived from constacyclic codes

Authors: Liqi Wang, Shixin Zhu

Published in: Quantum Information Processing | Issue 3/2015

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Abstract

Quantum maximum-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
$$\begin{aligned}{}[[\lambda (q-1),\lambda (q-1)-2d+2,d]]_q \end{aligned}$$
where \(2\le d\le (q+1)/2+\lambda -1\), and \(q+1=\lambda r\) with \(r\) even, and
$$\begin{aligned}{}[[\lambda (q-1),\lambda (q-1)-2d+2,d]]_q \end{aligned}$$
where \(2\le d\le (q+1)/2+\lambda /2-1\), and \(q+1=\lambda r\) with \(r\) odd. The quantum MDS codes exhibited here have parameters better than the ones available in the literature.

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Metadata
Title
New quantum MDS codes derived from constacyclic codes
Authors
Liqi Wang
Shixin Zhu
Publication date
01-03-2015
Publisher
Springer US
Published in
Quantum Information Processing / Issue 3/2015
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-014-0903-y