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 Modern Physics B

New optimal asymmetric quantum codes constructed from constacyclic codes

Genqi Xu, Ruihu Li, Luobin Guo, Liangdong Lü

Published Nov 24, 2016• 14 citations
Publisher

Abstract

In this paper, we propose the construction of asymmetric quantum codes from two families of constacyclic codes over finite field [Formula: see text] of code length [Formula: see text], where for the first family, [Formula: see text] is an odd prime power with the form [Formula: see text] ([Formula: see text] is integer) or [Formula: see text] ([Formula: see text] is integer) and [Formula: see text]; for the second family, [Formula: see text] is an odd prime power with the form [Formula: see text] or [Formula: see text] ([Formula: see text] is integer) and [Formula: see text]. As a result, families of new asymmetric quantum codes [Formula: see text] with [Formula: see text] distance larger than [Formula: see text] are obtained, which are not covered by the asymmetric quantum error-correcting codes (AQECCs) in Refs. 32 and 33 [J.-Z. Chen, J.-P. Li and J. Lin, Int. J. Theor. Phys. 53, 72 (2014); L. Wang and S. Zhu, Int. J. Quantum Inf. 12, 1450017 (2014)] that [Formula: see text]. Also, all the newly obtained asymmetric quantum codes are optimal according to the singleton bound for asymmetric quantum codes.

DOI
10.1142/s0217979217500308

Related papers

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 constacyclic codes with length n=2(qm+1)

Junli Wang, Ruihu Li, Yang Liu +1 more

By studying the properties of [Formula: see text]-cyclotomic cosets, the maximum designed distances of Hermitian dual-containing constacyclic Bose–Chaudhuri–Hocquenghem (BCH) codes with length [Formula: see text] are determined, where [Formula: see text] is an odd prime power and [Formula: see text] is an integer. Further, their dimensions are calculated precisely for the given designed distance. Consequently, via Hermitian Construction, many new quantum codes could be obtained from these codes, which are not covered in the literature.

International Journal of Quantum Information•Oct 1, 2019•5 citations

New nonbinary quantum codes with larger distance constructed from BCH codes over 𝔽q2

Genqi Xu, Ruihu Li, Qiang Fu +2 more

This paper concentrates on construction of new nonbinary quantum error-correcting codes (QECCs) from three classes of narrow-sense imprimitive BCH codes over finite field [Formula: see text] ([Formula: see text] is an odd prime power). By a careful analysis on properties of cyclotomic cosets in defining set [Formula: see text] of these BCH codes, the improved maximal designed distance of these narrow-sense imprimitive Hermitian dual-containing BCH codes is determined to be much larger than the result given according to Aly et al. [S. A. Aly, A. Klappenecker and P. K. Sarvepalli, IEEE Trans. Inf. Theory 53, 1183 (2007)] for each different code length. Thus families of new nonbinary QECCs are constructed, and the newly obtained QECCs have larger distance than those in previous literature.

International Journal of Modern Physics B•Dec 1, 2016•1 citation

Constacyclic codes over 𝔽 q 𝒮𝒯 and their applications

Amal S. Alali, Mohd Azmi, Nadeem ur Rehman +1 more

Let [Formula: see text], where p is an odd prime and r is a positive integer. Consider a ring [Formula: see text], where [Formula: see text] with [Formula: see text] and [Formula: see text] with [Formula: see text]. In this paper, we examine the algebraic structure of constacyclic codes over the ring [Formula: see text] of block length [Formula: see text]. Further, a construction of quantum error-correcting codes (QECCs) from constacyclic codes over [Formula: see text] is also given. Moreover, we derive a number of new QECCs.

AKCE International Journal of Graphs and Combinatorics•Sep 23, 2024•0 citations

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

Quantum error correction through constacyclic codes over mixed alphabet

Mohd Azmi, Mohammad Fareed Ahmad, Nadeem ur Rehman +1 more

Let q=pr, where p is an odd prime and r be a positive integer, 𝒮=𝔽q[u]〈u2−1〉 and 𝒯=𝔽q[u,v]〈u2−1,v2−1,uv=vu〉 and Ω=(ω1,ω2,ω3)∈𝔽q𝒮𝒯⁠. The algebraic structure of constacyclic codes over 𝔽q𝒮𝒯−Ω–constacyclic code of block length (l, m, n) is examined in this paper. The construction of quantum error-correcting codes (QECCs) from constacyclic codes over 𝔽q𝒮𝒯 is also covered in this paper and we derive some new QECCs.

AIP conference proceedings•Jan 1, 2026•0 citations
In this paper, we propose the construction of asymmetric quantum codes from two families of constacyclic codes over finite field [Formula: see text] of code length [Formula: see text], where for the first family, [Formula: see text] is an odd prime power with the form [Formula: see text] ([Formula: see text] is integer) or [Formula: see text] ([Formula: see text] is integer) and [Formula: see text]; for the second family, [Formula: see text] is an odd prime power with the form [Formula: see text] or [Formula: see text] ([Formula: see text] is integer) and [Formula: see text]. As a result, families of new asymmetric quantum codes [Formula: see text] with [Formula: see text] distance larger than [Formula: see text] are obtained, which are not covered by the asymmetric quantum error-correcting codes (AQECCs) in Refs. 32 and 33 [J.-Z. Chen, J.-P. Li and J. Lin, Int. J. Theor. Phys. 53, 72 (2014); L. Wang and S. Zhu, Int. J. Quantum Inf. 12, 1450017 (2014)] that [Formula: see text]. Also, all the newly obtained asymmetric quantum codes are optimal according to the singleton bound for asymmetric quantum codes.
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.
By studying the properties of [Formula: see text]-cyclotomic cosets, the maximum designed distances of Hermitian dual-containing constacyclic Bose–Chaudhuri–Hocquenghem (BCH) codes with length [Formula: see text] are determined, where [Formula: see text] is an odd prime power and [Formula: see text] is an integer. Further, their dimensions are calculated precisely for the given designed distance. Consequently, via Hermitian Construction, many new quantum codes could be obtained from these codes, which are not covered in the literature.
This paper concentrates on construction of new nonbinary quantum error-correcting codes (QECCs) from three classes of narrow-sense imprimitive BCH codes over finite field [Formula: see text] ([Formula: see text] is an odd prime power). By a careful analysis on properties of cyclotomic cosets in defining set [Formula: see text] of these BCH codes, the improved maximal designed distance of these narrow-sense imprimitive Hermitian dual-containing BCH codes is determined to be much larger than the result given according to Aly et al. [S. A. Aly, A. Klappenecker and P. K. Sarvepalli, IEEE Trans. Inf. Theory 53, 1183 (2007)] for each different code length. Thus families of new nonbinary QECCs are constructed, and the newly obtained QECCs have larger distance than those in previous literature.
Let [Formula: see text], where p is an odd prime and r is a positive integer. Consider a ring [Formula: see text], where [Formula: see text] with [Formula: see text] and [Formula: see text] with [Formula: see text]. In this paper, we examine the algebraic structure of constacyclic codes over the ring [Formula: see text] of block length [Formula: see text]. Further, a construction of quantum error-correcting codes (QECCs) from constacyclic codes over [Formula: see text] is also given. Moreover, we derive a number of new QECCs.
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.