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

IEEE Transactions on Information Theory

New Quantum MDS Codes

Giuliano G. La Guardia

Published Aug 1, 2011• 120 citations
Publisher

Abstract

New quantum maximum-distance-separable (MDS) codes with parameters [[q2+ 1,q2-2d+ 3,d]]q, whereq=2t,t≥ 1 and 3 ≤d≤q+1 is an odd integer, are constructed in this paper.
DOI
10.1109/tit.2011.2159039

Related papers

New quantum MDS codes

Guanghui Zhang, Bocong Chen

In this paper, we construct two classes of new quantum maximum-distance-separable (MDS) codes with parameters [Formula: see text], where q is an odd prime power with q ≡ 3 (mod 4) and [Formula: see text]; [[8(q - 1), 8(q - 1) - 2d + 2, d]]q, where q is an odd prime power with the form q = 8t - 1 (t is an even positive integer) and [Formula: see text]. Comparing the parameters with all known quantum MDS codes, the quantum MDS codes exhibited here have minimum distances bigger than the ones available in the literature.

International Journal of Quantum Information•Jun 1, 2014•43 citations

New Quantum MDS Codes From Negacyclic Codes

Xiaoshan Kai, Shixin Zhu

Letqbe an odd prime power. Based on classical negacyclic codes, we construct two classes of quantum maximum-distance-separable (MDS) codes with parameters [[q2+1,q2-2d+3,d]]qwhereq≡ 1 (mod 4) and 2 ≤d≤q+1 is even, and [[(q2+1)/2,(q2+1)/2-2d+2,d]]qwhere 3 ≤d≤qis odd. Some of these quantum MDS codes are new in the sense that their parameters are different from all the previously known ones.

IEEE Transactions on Information Theory•Sep 24, 2012•183 citations

A Construction of New Quantum MDS Codes

Lingfei Jin, Chaoping Xing

It has been a great challenge to construct new quantum maximum-distance-separable (MDS) codes. In particular, it is very hard to construct the quantum MDS codes with relatively large minimum distance. So far, except for some sparse lengths, all known q-ary quantum MDS codes have minimum distance ≤q/2 + 1. In this paper, we provide a construction of the quantum MDS codes with minimum distance >q/2 + 1. In particular, we show the existence of the q-ary quantum MDS codes with length n = q2+ 1 and minimum distance d for any d q + 1 (this result extends those given in the works of Guardia (2011), Jin et al. (2010), and Kai an Zhu (2012)); and with length (q2+ 2)/3 and minimum distance d for any d (2q+2)/3 if 3|(q + 1). Our method is through Hermitian selforthogonal codes. The main idea of constructing the Hermitian self-orthogonal codes is based on the solvability in Fqof a system of homogenous equations over Fq2.

arXiv:1311.3009•IEEE Transactions on Information Theory•Jan 31, 2014•108 citations

New Quantum MDS codes constructed from Constacyclic codes

Liangdong Lü, Wenping Ma, Ruihu Li +2 more

Quantum maximum-distance-separable (MDS) codes are an important class of quantum codes. In this paper, using constacyclic codes and Hermitain construction, we construct some new quantum MDS codes of the form $q=2am+t$, $n=\frac{q^{2}+1}{a}$. Most of these quantum MDS codes are new in the sense that their parameters are not covered be the codes available in the literature.

arXiv:1803.07927•Mar 20, 2018•5 citations

Construction of New q-ary quantum MDS codes with distance greater than $\frac{q}{2}$

Yu SHAO, Yindong Chen, Jingli WANG +1 more

In the past decade, the construction of quantum maximum-distance separable (MDS) codes has been extensively and deeply explored. For lengths of the form $n=\frac{q^2-1}{m}$, where m is an integer such that m|q+1 or m|q-1, comprehensive results are available. In this paper, we investigate the case where the length $n=\frac{q^2-1}{m}$, yet m is neither a divisor of q-1 nor q+1. Ultimately, this problem can be reduced to identifying the necessary and sufficient conditions for the existence of pairs (m1, m2), where $m=\frac{m_1\cdot m_2}{m_1+m_2-1}$ is an integer. In addition, the greatest common divisor of m with both m1 and m2, denoted as gcd(m, m1) and gcd(m, m2), must be greater than 1. The quantum MDS codes presented in this paper have not been previously investigated and their minimum distances exceed $\frac{q}{2}$.

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Jan 1, 2026•0 citations

On quantum MDS codes

Martin Rötteler, Markus Grassl, T. Beth

We construct maximum distance separable quantum error-correcting codes. The codes are defined over q-dimensional quantum systems, where q is any prime power. The construction yields quantum MDS codes of length up to q+1 for all possible dimensions and some quantum MDS codes of length up to q2+1. In particular, those families contain codes [[6,2,3]]pand [[7,3,3]]pfor pges3 (cf. [K. Feng (2002)])

IEEE International Symposium on Information Theory (ISIT)•Dec 23, 2004•55 citations
In this paper, we construct two classes of new quantum maximum-distance-separable (MDS) codes with parameters [Formula: see text], where q is an odd prime power with q ≡ 3 (mod 4) and [Formula: see text]; [[8(q - 1), 8(q - 1) - 2d + 2, d]]q, where q is an odd prime power with the form q = 8t - 1 (t is an even positive integer) and [Formula: see text]. Comparing the parameters with all known quantum MDS codes, the quantum MDS codes exhibited here have minimum distances bigger than the ones available in the literature.
It has been a great challenge to construct new quantum maximum-distance-separable (MDS) codes. In particular, it is very hard to construct the quantum MDS codes with relatively large minimum distance. So far, except for some sparse lengths, all known q-ary quantum MDS codes have minimum distance ≤q/2 + 1. In this paper, we provide a construction of the quantum MDS codes with minimum distance >q/2 + 1. In particular, we show the existence of the q-ary quantum MDS codes with length n = q2+ 1 and minimum distance d for any d q + 1 (this result extends those given in the works of Guardia (2011), Jin et al. (2010), and Kai an Zhu (2012)); and with length (q2+ 2)/3 and minimum distance d for any d (2q+2)/3 if 3|(q + 1). Our method is through Hermitian selforthogonal codes. The main idea of constructing the Hermitian self-orthogonal codes is based on the solvability in Fqof a system of homogenous equations over Fq2.
Quantum maximum-distance-separable (MDS) codes are an important class of quantum codes. In this paper, using constacyclic codes and Hermitain construction, we construct some new quantum MDS codes of the form q=2am+tq=2am+tq=2am+t, n=q2+1an=\frac{q^{2}+1}{a}n=aq2+1​. Most of these quantum MDS codes are new in the sense that their parameters are not covered be the codes available in the literature.
Construction of New q-ary quantum MDS codes with distance greater than q2\frac{q}{2}2q​
In the past decade, the construction of quantum maximum-distance separable (MDS) codes has been extensively and deeply explored. For lengths of the form n=q2−1mn=\frac{q^2-1}{m}n=mq2−1​, where m is an integer such that m|q+1 or m|q-1, comprehensive results are available. In this paper, we investigate the case where the length n=q2−1mn=\frac{q^2-1}{m}n=mq2−1​, yet m is neither a divisor of q-1 nor q+1. Ultimately, this problem can be reduced to identifying the necessary and sufficient conditions for the existence of pairs (m1, m2), where m=m1⋅m2m1+m2−1m=\frac{m_1\cdot m_2}{m_1+m_2-1}m=m1​+m2​−1m1​⋅m2​​ is an integer. In addition, the greatest common divisor of m with both m1 and m2, denoted as gcd(m, m1) and gcd(m, m2), must be greater than 1. The quantum MDS codes presented in this paper have not been previously investigated and their minimum distances exceed q2\frac{q}{2}2q​.