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 International Symposium on Information Theory (ISIT)

On quasi-cyclic codes

P. Heijnen, Henk van Tilborg, S. Weijs

Published Nov 27, 2002• 6 citations
Publisher

Abstract

Many binary quasi-cyclic codes have a better minimum distance than other known linear codes with the same parameters. We present 43 new quasi-cyclic codes, which improve on the parameters of previously found quasi-cyclic codes. Five of them even improve the lower bound on the minimum distance for linear codes. Furthermore we present a decoding algorithm for the binary quasi-cyclic codes of rate 1/m.

DOI
10.1109/isit.1998.708648

Related papers

New results on binary quasi-cyclic codes

Zhi Chen

Twelve new binary quasi-cyclic codes, which improve the lower bounds on minimum distances for binary linear codes, are presented, and a Web database on best-known binary quasi-cyclic codes is constructed for public access.

IEEE International Symposium on Information Theory (ISIT)•Nov 7, 2002•4 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

New binary linear codes

Thomas Aaron Gulliver, Patric R. J. Östergård

In this paper, nineteen new binary linear codes are presented which improve the bounds on the maximum possible minimum distance. These codes belong to the class of quasi-cyclic (QC) codes, and have been constructed using a stochastic optimization algorithm, tabu search. Six of the new codes meet the upper bound on minimum distance and so are optimal.

Ars Combinatoria•Jan 1, 2000•10 citations

Nine good rate (m-1)/pm quasi-cyclic codes

Thomas Aaron Gulliver, V.K. Bhargava

The class of quasi-cyclic (QC) codes has been proven to contain many good codes. To date the known results are largely codes of the form 1/p and (p-1)/p constructed from circulant matrices. A generalization of these rate 1/p codes to rate (m-1)/pm codes based on the theory of 1-generator QC codes is presented. The results of a search for good codes based on heuristic combinatorial optimization are nine codes which improve the known lower bounds on the minimum distance of binary linear codes.>

IEEE Transactions on Information Theory•Jul 1, 1992•41 citations

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

Liangdong Lü, Gaochi Zhang, FENG Ganyu +1 more

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.

International Symposium on AI and Cybersecurity (ISAICS)•Oct 24, 2025•0 citations

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
Many binary quasi-cyclic codes have a better minimum distance than other known linear codes with the same parameters. We present 43 new quasi-cyclic codes, which improve on the parameters of previously found quasi-cyclic codes. Five of them even improve the lower bound on the minimum distance for linear codes. Furthermore we present a decoding algorithm for the binary quasi-cyclic codes of rate 1/m.
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
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.