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

Constacyclic Codes and Some New Quantum MDS Codes

Xiaoshan Kai, Shixin Zhu, Li Ping

Published Feb 25, 2014• 213 citations
Publisher

Abstract

One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. Quantum maximal distance separable (MDS) codes are optimal in the sense they attain maximal minimum distance. Recently, constructing quantum MDS codes has received much attention and seems to become more and more difficult. In this paper, based on classical constacyclic codes, we construct some new quantum MDS codes by employing the Hermitian construction. Compared with the known quantum MDS codes, these quantum MDS codes have much larger minimum distance.

DOI
10.1109/tit.2014.2308180

Related papers

Some New Classes of Quantum MDS Codes From Constacyclic Codes

Tao Zhang, Gennian Ge

Quantum maximum-distance-separable (MDS) codes form an important family of quantum codes. In this paper, using Hermitian construction and classical constacyclic codes, we construct six classes of quantum MDS codes. Two of these six classes of quantum MDS codes have larger minimum distance than the ones available in the literature. Most of these quantum MDS codes are new in the sense that their parameters are not covered by the codes available in the literature.

IEEE Transactions on Information Theory•Jul 21, 2015•66 citations

Construction of new quantum MDS codes derived from constacyclic codes

Divya Taneja, Manish K. Gupta, Rajesh Kumar Narula +1 more

Obtaining quantum maximum distance separable (MDS) codes from dual containing classical constacyclic codes using Hermitian construction have paved a path to undertake the challenges related to such constructions. Using the same technique, some new parameters of quantum MDS codes have been constructed here. One set of parameters obtained in this paper has achieved much larger distance than work done earlier. The remaining constructed parameters of quantum MDS codes have large minimum distance and were not explored yet.

International Journal of Quantum Information•Dec 29, 2016•5 citations

Some new quantum MDS codes with large minimum distance

Lanqiang Li, Fuyin Tian, Ziwen Cao +1 more

Abstract The construction of quantum Maximum Distance Separable (MDS) error-correcting codes is of great significance in practical applications, as it plays a vital role in enhancing the reliability and efficiency of quantum communication and quantum computing. As a result, it remains an active research topic in the field of quantum information science. In this paper, based on generalized Reed-Solomon (GRS) codes and Hermitian construction, we construct two new classes of quantum MDS codes. Our constructed quantum MDS codes are novel in the sense that their parameters differ from all previously known codes. Furthermore, most of our codes exhibit significantly larger minimum distance compared to the existing ones of the same length.

•Feb 5, 2024•0 citations

Application of Constacyclic Codes to Quantum MDS Codes

Bocong Chen, San Ling, Guanghui Zhang

Quantum maximum-distance-separable (MDS) codes form an important class of quantum codes. To get q-ary quantum MDS codes, one of the effective ways is to find linear MDS codes C over Fq2satisfying C⊥H⊆ C, where C⊥Hdenotes the Hermitian dual code of C. For a linear code C of length n over Fq2, we say that C is a dual-containing code if C⊥H⊆ C and C≠ Fq2n. Several classes of new quantum MDS codes with relatively large minimum distance have been produced through dual-containing constacyclic MDS codes. These works motivate us to make a careful study on the existence conditions for dual-containing constacyclic codes. We obtain necessary and sufficient conditions for the existence of dual-containing constacyclic codes. Four classes of dual-containing constacyclic MDS codes are constructed and their parameters are computed. Consequently, the quantum MDS codes are derived from these parameters. The quantum MDS codes exhibited here have minimum distance bigger than the ones available in the literature.

arXiv:1403.2499•IEEE Transactions on Information Theory•Jan 7, 2015•191 citations

Some families of optimal quantum codes derived from constacyclic codes

Jian‐Zhang Chen, Yuanyuan Huang, Chunhui Feng +1 more

Quantum maximum-distance-separable (MDS) codes form an important family of quantum codes. Quantum MDS codes are optimal, which can attain the quantum Singleton bound. In this paper, using some classes of constacyclic codes and Hermitian constructions, we propose the constructions of optimal quantum convolutional codes and optimal asymmetric quantum codes in the sense of the quantum Singleton bound. Compared with the codes obtained in the literature, the parameters of the constructed quantum codes are new as well as the distance dz of optimal asymmetric quantum codes [[n,k,dz/dx]]q2 constructed in this paper is larger.

Linear and Multilinear Algebra•Feb 5, 2018•8 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
One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. Quantum maximal distance separable (MDS) codes are optimal in the sense they attain maximal minimum distance. Recently, constructing quantum MDS codes has received much attention and seems to become more and more difficult. In this paper, based on classical constacyclic codes, we construct some new quantum MDS codes by employing the Hermitian construction. Compared with the known quantum MDS codes, these quantum MDS codes have much larger minimum distance.
Obtaining quantum maximum distance separable (MDS) codes from dual containing classical constacyclic codes using Hermitian construction have paved a path to undertake the challenges related to such constructions. Using the same technique, some new parameters of quantum MDS codes have been constructed here. One set of parameters obtained in this paper has achieved much larger distance than work done earlier. The remaining constructed parameters of quantum MDS codes have large minimum distance and were not explored yet.
Abstract The construction of quantum Maximum Distance Separable (MDS) error-correcting codes is of great significance in practical applications, as it plays a vital role in enhancing the reliability and efficiency of quantum communication and quantum computing. As a result, it remains an active research topic in the field of quantum information science. In this paper, based on generalized Reed-Solomon (GRS) codes and Hermitian construction, we construct two new classes of quantum MDS codes. Our constructed quantum MDS codes are novel in the sense that their parameters differ from all previously known codes. Furthermore, most of our codes exhibit significantly larger minimum distance compared to the existing ones of the same length.
Quantum maximum-distance-separable (MDS) codes form an important class of quantum codes. To get q-ary quantum MDS codes, one of the effective ways is to find linear MDS codes C over Fq2satisfying C⊥H⊆ C, where C⊥Hdenotes the Hermitian dual code of C. For a linear code C of length n over Fq2, we say that C is a dual-containing code if C⊥H⊆ C and C≠ Fq2n. Several classes of new quantum MDS codes with relatively large minimum distance have been produced through dual-containing constacyclic MDS codes. These works motivate us to make a careful study on the existence conditions for dual-containing constacyclic codes. We obtain necessary and sufficient conditions for the existence of dual-containing constacyclic codes. Four classes of dual-containing constacyclic MDS codes are constructed and their parameters are computed. Consequently, the quantum MDS codes are derived from these parameters. The quantum MDS codes exhibited here have minimum distance bigger than the ones available in the literature.
Quantum maximum-distance-separable (MDS) codes form an important family of quantum codes. Quantum MDS codes are optimal, which can attain the quantum Singleton bound. In this paper, using some classes of constacyclic codes and Hermitian constructions, we propose the constructions of optimal quantum convolutional codes and optimal asymmetric quantum codes in the sense of the quantum Singleton bound. Compared with the codes obtained in the literature, the parameters of the constructed quantum codes are new as well as the distance dz of optimal asymmetric quantum codes [[n,k,dz/dx]]q2 constructed in this paper is larger.
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.