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

International Journal of Quantum Information

New quantum MDS codes

Guanghui Zhang, Bocong Chen

Published Jun 1, 2014• 43 citations
Publisher

Abstract

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.

DOI
10.1142/s0219749914500191

Related papers

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

Exploring new lengths for q-ary quantum MDS codes with larger distance

Xianmang He, Jingli Wang, Chunfang Huang +1 more

In the past decade, the construction of quantum maximum distance separable codes (MDS for short) has been extensively studied. For the length [Formula: see text], where m is an integer that divides either q + 1 or q - 1, a complete set of results has been available. In this paper, we dedicate to a previously unexplored cases where the length [Formula: see text], subject to the conditions that m is neither a divisor of q - 1 nor q + 1. Ultimately, this problem can be summarized as exploring the necessary and sufficient conditions for the existence of pairs [Formula: see text], where [Formula: see text] is an integer, with the additional requirement that the greatest common divisor ([Formula: see text]) of m with both m1 and m2, [Formula: see text] and [Formula: see text], and [Formula: see text]. The quantum MDS codes presented herein are novel and exhibit distance parameters exceeding [Formula: see text].

PLoS ONE•Jun 5, 2025•0 citations

Construction of quantum MDS codes from generalized Reed–Solomon codes

Mingwei Lu, Shixin Zhu

Quantum maximum-distance-separable (MDS) codes play an important role in the quantum codes. The previous quantum MDS codes had been constructed according to [Formula: see text] is odd or even. However, such classification omits to consider some special categories of quantum MDS codes. Because of this, we will discuss the other classifications of [Formula: see text]. In this paper, we construct some new [Formula: see text]-ary quantum MDS codes from generalized Reed–Solomon codes by using Hermitian construction, and prove that these quantum MDS codes have minimum distance greater than [Formula: see text], where [Formula: see text].

International Journal of Quantum Information•Apr 17, 2023•3 citations

New optimal asymmetric quantum codes from constacyclic codes

Guanghui Zhang, Bocong Chen, Liangchen Li

In this paper, we construct two classes of asymmetric quantum codes by using constacyclic codes. The first class is the asymmetric quantum codes with parameters [[q2 + 1, q2 + 1 - 2(t + k + 1), (2k + 2)/(2t + 2)]]q2 where q is an odd prime power, t, k are integers with [Formula: see text], which is a generalization of [J. Chen, J. Li and J. Lin, Int. J. Theor. Phys. 53 (2014) 72, Theorem 2] in the sense that we do not assume that q ≡1 ( mod 4). The second one is the asymmetric quantum codes with parameters [Formula: see text], where q ≥ 5 is an odd prime power, t, k are integers with 0 ≤ t ≤ k ≤ q - 1. The constructed asymmetric quantum codes are optimal and their parameters are not covered by the codes available in the literature.

Modern Physics Letters B•Jun 17, 2014•14 citations

New Quantum MDS Codes

Giuliano G. La Guardia

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.

IEEE Transactions on Information Theory•Aug 1, 2011•120 citations

New entanglement-assisted quantum MDS codes derived from cyclic codes

Sujuan Huang, Shixin Zhu, Pan Wang

Entanglement-assisted quantum error-correcting codes, which can be seen as a generalization of quantum error-correcting codes, can be constructed from arbitrary classical linear codes by relaxing the self-orthogonality properties and using pre-shared entangled states between the sender and the receiver, and can also improve the performance of quantum error-correcting codes. In this paper, we construct some families of entanglement-assisted quantum maximum-distance-separable codes with parameters $[[\frac{{{q^2} - 1}}{a},\frac{{{q^2} - 1}}{a} - 2d+2 + c,d;c]]_q$, where $q$ is a prime power with the form $q = am \pm \ell$, $a = \frac{{\ell^2} - 1}{3}$ is an odd integer, $\ell \equiv 2\ (\bmod\ 6)$ or $\ell \equiv 4\ (\bmod\ 6)$, and $m$ is a positive integer. Most of these codes are new in the sense that their parameters are not covered by the codes available in the literature.

Quantum Information and Computation•Apr 1, 2023•0 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.
In the past decade, the construction of quantum maximum distance separable codes (MDS for short) has been extensively studied. For the length [Formula: see text], where m is an integer that divides either q + 1 or q - 1, a complete set of results has been available. In this paper, we dedicate to a previously unexplored cases where the length [Formula: see text], subject to the conditions that m is neither a divisor of q - 1 nor q + 1. Ultimately, this problem can be summarized as exploring the necessary and sufficient conditions for the existence of pairs [Formula: see text], where [Formula: see text] is an integer, with the additional requirement that the greatest common divisor ([Formula: see text]) of m with both m1 and m2, [Formula: see text] and [Formula: see text], and [Formula: see text]. The quantum MDS codes presented herein are novel and exhibit distance parameters exceeding [Formula: see text].
Quantum maximum-distance-separable (MDS) codes play an important role in the quantum codes. The previous quantum MDS codes had been constructed according to [Formula: see text] is odd or even. However, such classification omits to consider some special categories of quantum MDS codes. Because of this, we will discuss the other classifications of [Formula: see text]. In this paper, we construct some new [Formula: see text]-ary quantum MDS codes from generalized Reed–Solomon codes by using Hermitian construction, and prove that these quantum MDS codes have minimum distance greater than [Formula: see text], where [Formula: see text].
In this paper, we construct two classes of asymmetric quantum codes by using constacyclic codes. The first class is the asymmetric quantum codes with parameters [[q2 + 1, q2 + 1 - 2(t + k + 1), (2k + 2)/(2t + 2)]]q2 where q is an odd prime power, t, k are integers with [Formula: see text], which is a generalization of [J. Chen, J. Li and J. Lin, Int. J. Theor. Phys. 53 (2014) 72, Theorem 2] in the sense that we do not assume that q ≡1 ( mod 4). The second one is the asymmetric quantum codes with parameters [Formula: see text], where q ≥ 5 is an odd prime power, t, k are integers with 0 ≤ t ≤ k ≤ q - 1. The constructed asymmetric quantum codes are optimal and their parameters are not covered by the codes available in the literature.
Entanglement-assisted quantum error-correcting codes, which can be seen as a generalization of quantum error-correcting codes, can be constructed from arbitrary classical linear codes by relaxing the self-orthogonality properties and using pre-shared entangled states between the sender and the receiver, and can also improve the performance of quantum error-correcting codes. In this paper, we construct some families of entanglement-assisted quantum maximum-distance-separable codes with parameters [[q2−1a,q2−1a−2d+2+c,d;c]]q[[\frac{{{q^2} - 1}}{a},\frac{{{q^2} - 1}}{a} - 2d+2 + c,d;c]]_q[[aq2−1​,aq2−1​−2d+2+c,d;c]]q​, where qqq is a prime power with the form q=am±ℓq = am \pm \ellq=am±ℓ, a=ℓ2−13a = \frac{{\ell^2} - 1}{3}a=3ℓ2−1​ is an odd integer, ℓ≡2 ( mod  6)\ell \equiv 2\ (\bmod\ 6)ℓ≡2 (mod 6) or ℓ≡4 ( mod  6)\ell \equiv 4\ (\bmod\ 6)ℓ≡4 (mod 6), and mmm is a positive integer. Most of these codes are new in the sense that their parameters are not covered by the codes available in the literature.