Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1508.00978

Quantum Codes from Generalized Reed-Solomon Codes and Matrix-Product Codes

Tao Zhang, Gennian Ge

Published Aug 5, 2015• 7 citations
arXivHTMLPDF

Abstract

One of the central tasks in quantum error-correction is to construct quantum codes that have good parameters. In this paper, we construct three new classes of quantum MDS codes from classical Hermitian self-orthogonal generalized Reed-Solomon codes. We also present some classes of quantum codes from matrix-product codes. It turns out that many of our quantum codes are new in the sense that the parameters of quantum codes cannot be obtained from all previous constructions.

DOI
10.48550/arxiv.1508.00978

Related papers

Two new classes of quantum MDS codes from generalized Reed-Solomon codes

Weiwei Wang, Jiantao Li

In this paper, we mainly use classical Hermitian self-orthogonal generalized Reed-Solomon codes to construct two new classes of quantum MDS codes. Most of our quantum MDS codes have minimum distance larger than q/2+1. Compared with previously known constructions, these quantum MDS codes in our constructions have large minimum distance and their parameters are not covered by the previous codes.

arXiv:2001.03445•Jan 6, 2020•0 citations

New Quantum MDS codes from Hermitian self-orthogonal generalized Reed-Solomon codes

Ruhao Wan, Shixin Zhu

Quantum maximum-distance-separable (MDS for short) codes are an important class of quantum codes. In this paper, by using Hermitian self-orthogonal generalized Reed-Solomon (GRS for short) codes, we construct five new classes of $q$-ary quantum MDS codes with minimum distance larger than $q/2+1$. Furthermore, the parameters of our quantum MDS code cannot be obtained from the previous constructions.

arXiv:2302.06169•Feb 13, 2023•0 citations

Some quantum MDS codes from GRS codes

Guohui Wang, Chunming Tang

The construction of quantum maximum-distance-separable (MDS) codes has become one of the major goals in quantum coding theory. In this paper, we construct several classes of Hermitian self-orthogonal generalized Reed–Solomon codes. Based on these classical MDS codes, we obtain several new classes of quantum MDS codes with large minimum distance. It turns out that these constructed quantum MDS codes have fewer constraints on the selection of code length, and in some cases, have larger minimum distance than previous literature. Notably, some of the distance parameters of our codes are greater than (q/2)+1.

Linear and Multilinear Algebra•Feb 25, 2023•3 citations

Two new classes of Hermitian self-orthogonal non-GRS MDS codes and their applications

Gaojun Luo, Xiwang Cao, Martianus Frederic Ezerman +1 more

Hermitian self-orthogonal codes form an essential ingredient in the construction of quantum stabilizer codes. In this paper, we present two new classes of Hermitian self-orthogonal MDS codes from twisted generalized Reed-Solomon codes. The constructed codes are monomially inequivalent to generalized Reed-Solomon codes. Two new classes of Hermitian LCD MDS codes can then be derived. Finally, based on the constructed Hermitian self-orthogonal MDS codes, we present two classes of quantum MDS codes with new parameters.

Advances in Mathematics of Communications•Jan 1, 2022•4 citations

Some new quantum MDS codes derived from generalized Reed-Solomon codes

Xueying Shi, Qin Yue

Quantum maximum-distance-separable (MDS) codes are very important in coding theory. In this paper, we construct three classes of new quantum MDS codes with large minimum distance by classical Hermitian self-orthogonal generalized Reed-Solomon codes. Furthermore, these quantum MDS codes have more flexible lengths and larger minimum distance than those of some known quantum MDS codes.

Advances in Mathematics of Communications•Jan 1, 2022•5 citations

Some New Constructions of Quantum MDS Codes

Weijun Fang, Fang‐Wei Fu

It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes of$q$-ary quantum MDS codes by using generalized Reed–Solomon (GRS) codes and Hermitian construction. The minimum distances of our quantum MDS codes can be larger than$\frac {q}{2}+1$. Three of these six classes of quantum MDS codes have longer lengths than the ones constructed in[1]and[2], hence some of their results can be easily derived from ours via the propagation rule. Moreover, some known quantum MDS codes of specific lengths can be seen as special cases of ours and the minimum distances of some known quantum MDS codes are also improved as well.

arXiv:1804.08213•IEEE Transactions on Information Theory•Sep 3, 2019•58 citations
One of the central tasks in quantum error-correction is to construct quantum codes that have good parameters. In this paper, we construct three new classes of quantum MDS codes from classical Hermitian self-orthogonal generalized Reed-Solomon codes. We also present some classes of quantum codes from matrix-product codes. It turns out that many of our quantum codes are new in the sense that the parameters of quantum codes cannot be obtained from all previous constructions.
Quantum maximum-distance-separable (MDS for short) codes are an important class of quantum codes. In this paper, by using Hermitian self-orthogonal generalized Reed-Solomon (GRS for short) codes, we construct five new classes of qqq-ary quantum MDS codes with minimum distance larger than q/2+1q/2+1q/2+1. Furthermore, the parameters of our quantum MDS code cannot be obtained from the previous constructions.
The construction of quantum maximum-distance-separable (MDS) codes has become one of the major goals in quantum coding theory. In this paper, we construct several classes of Hermitian self-orthogonal generalized Reed–Solomon codes. Based on these classical MDS codes, we obtain several new classes of quantum MDS codes with large minimum distance. It turns out that these constructed quantum MDS codes have fewer constraints on the selection of code length, and in some cases, have larger minimum distance than previous literature. Notably, some of the distance parameters of our codes are greater than (q/2)+1.
Hermitian self-orthogonal codes form an essential ingredient in the construction of quantum stabilizer codes. In this paper, we present two new classes of Hermitian self-orthogonal MDS codes from twisted generalized Reed-Solomon codes. The constructed codes are monomially inequivalent to generalized Reed-Solomon codes. Two new classes of Hermitian LCD MDS codes can then be derived. Finally, based on the constructed Hermitian self-orthogonal MDS codes, we present two classes of quantum MDS codes with new parameters.
It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes ofqqq-ary quantum MDS codes by using generalized Reed–Solomon (GRS) codes and Hermitian construction. The minimum distances of our quantum MDS codes can be larger thanq2+1\frac {q}{2}+12q​+1. Three of these six classes of quantum MDS codes have longer lengths than the ones constructed in[1]and[2], hence some of their results can be easily derived from ours via the propagation rule. Moreover, some known quantum MDS codes of specific lengths can be seen as special cases of ours and the minimum distances of some known quantum MDS codes are also improved as well.