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 Conference on Modeling, Natural Language Processing and Machine Learning (CMNM)

Some new classes of quantum convolutional and asymmetric MDS codes

Weiwei Wang, Jiantao Li

Published May 17, 2024• 0 citations
Publisher

Abstract

Recently, considerable works of literature have grown up around the theme of quantum error-correcting codes. Quantum convolutional maximum distance separable (MDS for brevity) codes and MDS asymmetric quantum codes often have better properties in long-distance quantum communications and asymmetric quantum channels. Within this writing, the authors utilized constacyclic codes in constructing three new kinds of MDS quantum convolutional codes and a class of MDS asymmetric quantum codes. These results are new in comparison with those presented in the existing publications on this subject.

DOI
10.1145/3677779.3677805

Related papers

Constacyclic Codes and Some New Quantum MDS Codes

Xiaoshan Kai, Shixin Zhu, Li Ping

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.

IEEE Transactions on Information Theory•Feb 25, 2014•213 citations

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

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

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 new QEC MDS codes with large minimum distance

Lanqiang Li, Fuyin Tian, Ziwen Cao +1 more

The advancement of Quantum Error-Correcting (QEC) Maximum Distance Separable (MDS) codes holds substantial importance in practical applications, substantially augmenting the reliability and efficiency of quantum communication and computing. This paper introduces two new classes of QEC MDS codes, which are devised through the utilization of generalized Reed-Solomon (GRS) codes and the Hermitian construction approach. The novelty of our QEC MDS codes lies in their parameters being distinct from all previously reported codes. Moreover, most of our codes possess a considerably greater minimum distance in comparison to existing codes of the same length.

Scientific Reports•Jul 1, 2025•0 citations

New entanglement-assisted MDS quantum constacyclic codes

Hangyu Liu, Sujuan Huang, Liqi Wang +1 more

Entanglement-assisted quantum error-correcting codes can be seen as a new-type of quantum error-correcting codes and can be constructed from arbitrary linear codes which should not satisfy the dual-containing condition by utilizing shared entangled states between the sender and the receiver in advance. In this paper, we construct several new classes of entanglement-assisted quantum maximum-distance-separable codes from constacyclic codes and cyclic codes by exploiting small pre-shared entangled states, respectively. These codes are new in the sense that they are not covered by the codes available in the literature.

Quantum Information and Computation•Sep 1, 2024•0 citations
Recently, considerable works of literature have grown up around the theme of quantum error-correcting codes. Quantum convolutional maximum distance separable (MDS for brevity) codes and MDS asymmetric quantum codes often have better properties in long-distance quantum communications and asymmetric quantum channels. Within this writing, the authors utilized constacyclic codes in constructing three new kinds of MDS quantum convolutional codes and a class of MDS asymmetric quantum codes. These results are new in comparison with those presented in the existing publications on this subject.
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.
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.
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.
The advancement of Quantum Error-Correcting (QEC) Maximum Distance Separable (MDS) codes holds substantial importance in practical applications, substantially augmenting the reliability and efficiency of quantum communication and computing. This paper introduces two new classes of QEC MDS codes, which are devised through the utilization of generalized Reed-Solomon (GRS) codes and the Hermitian construction approach. The novelty of our QEC MDS codes lies in their parameters being distinct from all previously reported codes. Moreover, most of our codes possess a considerably greater minimum distance in comparison to existing codes of the same length.
Entanglement-assisted quantum error-correcting codes can be seen as a new-type of quantum error-correcting codes and can be constructed from arbitrary linear codes which should not satisfy the dual-containing condition by utilizing shared entangled states between the sender and the receiver in advance. In this paper, we construct several new classes of entanglement-assisted quantum maximum-distance-separable codes from constacyclic codes and cyclic codes by exploiting small pre-shared entangled states, respectively. These codes are new in the sense that they are not covered by the codes available in the literature.