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 Symposium on AI and Cybersecurity (ISAICS)

New binary quantum codes from Hermitian dual-containing Quasi-cyclic codes

Liangdong Lü, Gaochi Zhang, FENG Ganyu, Wenzheng Ma

Published Oct 24, 2025• 0 citations
Publisher

Abstract

In this paper, we introduce a class of dualcontaining 2 -generator quasi-cyclic codes over $G F(4)$. By Hermitian construction, we show computation constructions of binary quantum codes with good parameters from quaternary quasi-cyclic codes. Furthermore, 3 new quantum codes [[42, 10, 9]], [[74,,36, 9]] and [[78, 40, 9]] are derived from Hermitian dual-containing quasi-cyclic codes by an exhaustive search, along with 24 newly derived codes that enhance the previously best-known lower bounds on minimum distance.

DOI
10.1109/isaics66888.2025.11350081

Related papers

Quasi-cyclic Hermitian construction of binary quantum codes

Liangdong Lü, Zhang, Gaochi, Feng, Ganyu +1 more

In this paper, we propose a sufficient condition for a family of 2-generator self-orthogonal quasi-cyclic codes with respect to Hermitian inner product. Supported in the Hermitian construction, we show algebraic constructions of good quantum codes. 30 new binary quantum codes with good parameters improving the best-known lower bounds on minimum distance in Grassl's code tables \cite{Grassl:codetables} are constructed.

arXiv:2210.04487•Oct 10, 2022•0 citations

Lower Bounds for Quasi-Cyclic Codes and New Binary Quantum Codes

Yiting Liu, Chaofeng Guan, Chao Du +1 more

This paper considers three kinds of quasi-cyclic codes of index two with one generator or two generators and their applications in quantum code construction. In accordance with the algebraic structure of linear codes, we determine the lower bounds of the symplectic weights of these quasi-cyclic codes. Quasi-cyclic codes with the dual-containing property enable the construction of quantum codes. Defining the coefficient symmetric polynomials of the generator polynomials gives a concise condition for the dual-containing of the quasi-cyclic codes. The lower bound results can significantly reduce the scope of the search for a larger minimum distance of quasi-cyclic codes. With these algebraic results and computer supports, we obtain classical quasi-cyclic codes with better parameters and some new quantum codes under the symplectic construction. In particular, two examples of the new quantum codes [[63,42,6]]2,[[51,35,5]]2 improve the corresponding codes in Grassl’s code table.

Symmetry•Mar 3, 2023•5 citations

New quantum codes from self-dual codes over F_4

Reza Dastbasteh, Petr Lisoněk

We present new constructions of binary quantum codes from quaternary linear Hermitian self-dual codes. Our main ingredients for these constructions are nearly self-orthogonal cyclic or duadic codes over F_4. An infinite family of $0$-dimensional binary quantum codes is provided. We give minimum distance lower bounds for our quantum codes in terms of the minimum distance of their ingredient linear codes. We also present new results on the minimum distance of linear cyclic codes using their fixed subcodes. Finally, we list many new record-breaking quantum codes obtained from our constructions.

arXiv:2211.00891•Nov 2, 2022•1 citation

New Binary Quantum Codes Derived From One-Generator Quasi-Cyclic Codes

Jingjie Lv, Ruihu Li, Junli Wang

In this paper, we consider a family of one-generator quasi-cyclic (QC) codes and their applications in quantum codes construction. We give a sufficient condition for one-generator QC codes to be self-orthogonal with respect to the symplectic inner product. As the computational results, five new binary quantum codes with parameters [[45,29,5]], [[63,36,7]], [[73,55,5]], [[105,71,7]], and [[105,72,7]] improving the best-known lower bounds on minimum distance in Grassl's code tables are constructed.

IEEE Access•Jan 1, 2019•29 citations

An Explicit Construction of Quantum Stabilizer Codes From Quasi-Cyclic Codes

Jingjie Lv, Ruihu Li, Junli Wang

In this short letter, our main objective is to construct good quantum stabilizer codes over small fields, which have a more potential possibility to be employed in actual quantum processors. We firstly consider a suitable class of two-generators quasi-cyclic (QC) codes and determine their parameters. Then by virtue of their symplectic dual algebraic structure, we derive a sufficient condition to be symplectic dual-containing of these codes. Subsequently, an explicit construction of stabilizer codes from quasi-cyclic codes is presented. As for computational results, we provide many stabilizer codes with good parameters over binary, ternary and quaternary fields that all can not be deduced by the quantum Gilbert-Varshamov (GV) bound. In the binary case, our several codes strictly improve the lower bounds on the minimum distance in current records. In the ternary and quaternary occasions, numerous codes fill some gaps or have better parameters than the current results.

IEEE Communications Letters•Mar 2, 2020•21 citations

Some new binary codes with improved minimum distances

Eric Z. Chen

It has been well-known that the class of quasi-cyclic (QC) codes contain many good codes. In this paper, a method to conduct a computer search for binary $2$-generator QC codes is presented, and a large number of good $2$-generator QC codes have been obtained. $5$ new binary QC codes that improve the lower bounds on minimum distance are presented. Furthermore, with new $2$-generator QC codes and Construction X, $2$ new improved binary linear codes are obtained. With the standard construction techniques, another $16$ new binary linear codes that improve the lower bound on the minimum distance have also been obtained. Received: 9 November 2016 Accepted: 22 November 2017

Journal of Algebra Combinatorics Discrete Structures and Applications•Mar 13, 2018•6 citations
In this paper, we introduce a class of dualcontaining 2 -generator quasi-cyclic codes over GF(4)G F(4)GF(4). By Hermitian construction, we show computation constructions of binary quantum codes with good parameters from quaternary quasi-cyclic codes. Furthermore, 3 new quantum codes [[42, 10, 9]], [[74,,36, 9]] and [[78, 40, 9]] are derived from Hermitian dual-containing quasi-cyclic codes by an exhaustive search, along with 24 newly derived codes that enhance the previously best-known lower bounds on minimum distance.
This paper considers three kinds of quasi-cyclic codes of index two with one generator or two generators and their applications in quantum code construction. In accordance with the algebraic structure of linear codes, we determine the lower bounds of the symplectic weights of these quasi-cyclic codes. Quasi-cyclic codes with the dual-containing property enable the construction of quantum codes. Defining the coefficient symmetric polynomials of the generator polynomials gives a concise condition for the dual-containing of the quasi-cyclic codes. The lower bound results can significantly reduce the scope of the search for a larger minimum distance of quasi-cyclic codes. With these algebraic results and computer supports, we obtain classical quasi-cyclic codes with better parameters and some new quantum codes under the symplectic construction. In particular, two examples of the new quantum codes [[63,42,6]]2,[[51,35,5]]2 improve the corresponding codes in Grassl’s code table.
We present new constructions of binary quantum codes from quaternary linear Hermitian self-dual codes. Our main ingredients for these constructions are nearly self-orthogonal cyclic or duadic codes over F_4. An infinite family of 000-dimensional binary quantum codes is provided. We give minimum distance lower bounds for our quantum codes in terms of the minimum distance of their ingredient linear codes. We also present new results on the minimum distance of linear cyclic codes using their fixed subcodes. Finally, we list many new record-breaking quantum codes obtained from our constructions.
In this paper, we consider a family of one-generator quasi-cyclic (QC) codes and their applications in quantum codes construction. We give a sufficient condition for one-generator QC codes to be self-orthogonal with respect to the symplectic inner product. As the computational results, five new binary quantum codes with parameters [[45,29,5]], [[63,36,7]], [[73,55,5]], [[105,71,7]], and [[105,72,7]] improving the best-known lower bounds on minimum distance in Grassl's code tables are constructed.
In this short letter, our main objective is to construct good quantum stabilizer codes over small fields, which have a more potential possibility to be employed in actual quantum processors. We firstly consider a suitable class of two-generators quasi-cyclic (QC) codes and determine their parameters. Then by virtue of their symplectic dual algebraic structure, we derive a sufficient condition to be symplectic dual-containing of these codes. Subsequently, an explicit construction of stabilizer codes from quasi-cyclic codes is presented. As for computational results, we provide many stabilizer codes with good parameters over binary, ternary and quaternary fields that all can not be deduced by the quantum Gilbert-Varshamov (GV) bound. In the binary case, our several codes strictly improve the lower bounds on the minimum distance in current records. In the ternary and quaternary occasions, numerous codes fill some gaps or have better parameters than the current results.
It has been well-known that the class of quasi-cyclic (QC) codes contain many good codes. In this paper, a method to conduct a computer search for binary 222-generator QC codes is presented, and a large number of good 222-generator QC codes have been obtained. 555 new binary QC codes that improve the lower bounds on minimum distance are presented. Furthermore, with new 222-generator QC codes and Construction X, 222 new improved binary linear codes are obtained. With the standard construction techniques, another 161616 new binary linear codes that improve the lower bound on the minimum distance have also been obtained. Received: 9 November 2016 Accepted: 22 November 2017