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

arXiv:2405.06292 · Cryptography and Communications

On general self-orthogonal matrix-product codes associated with Toeplitz matrices

Yang Li, Shixin Zhu, Edgar Martı́nez-Moro

Published Dec 5, 2024• 0 citations
arXivHTMLPDF
DOI
10.1007/s12095-024-00763-6

Related papers

Hermitian self-orthogonal matrix product codes and their applications to quantum codes

Xiaoyan Zhang

Quantum Information Processing•Mar 15, 2024•5 citations

Matrix-product constructions for Galois self-orthogonal codes and new quantum codes

Liqi Wang, Xinxin Zhang, Shixin Zhu

Computational and Applied Mathematics•Jul 22, 2025•2 citations

Properties and Comparisons of Various Graphs and Their Codes

Andreas Garcia, Layla Jarrahy, Elisaveta Samoylov

It is established in literature that finding stabilizer quantum error correcting codes (QECCS) is the same as finding self-dual additive codes over the finite field $\mathbb{F}_{4}$ under the Hermitian trace inner product. Additionally, every self-dual additive code can be represented by a graph adjacency matrix. Many selfdual additive codes are constructed from circulant graphs. We introduce new graph code constructions: the Toeplitz Graph, the Multidimensional Toeplitz Graph (MDT), and the Generalized Toeplitz (GT) graph constructions. We consider some of the properties of the Toeplitz and Multidimensional Toeplitz Graphs and compare the Circulant and GT code constructions.

IEEE MIT Undergraduate Research Technology Conference (URTC)•Oct 11, 2024•0 citations

Quantum error-correcting codes from matrix-product codes related to quasi-orthogonal matrices and quasi-unitary matrices.

Meng Cao

Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite fields. The construction of matrix-product codes with certain self-orthogonality over finite fields is an effective way to obtain good $q$-ary quantum codes of large length. Specifically, it follows from CSS construction (resp. Hermitian construction) that a matrix-product code over $\mathbb{F}_{q}$ (resp. $\mathbb{F}_{q^{2}}$) which is Euclidean dual-containing (resp. Hermitian dual-containing) can produce a $q$-ary quantum code. In order to obtain such matrix-product codes, a common way is to construct quasi-orthogonal matrices (resp. quasi-unitary matrices) as the defining matrices of matrix-product codes over $\mathbb{F}_{q}$ (resp. $\mathbb{F}_{q^{2}}$). The usage of NSC quasi-orthogonal matrices or NSC quasi-unitary matrices in this process enables the minimum distance lower bound of the corresponding quantum codes to reach its optimum. This article has two purposes: the first is to summarize some results of this topic obtained by the author of this article and his cooperators in \cite{Cao2020Constructioncaowang,Cao2020New,Cao2020Constructionof}; the second is to add some new results on quasi-orthogonal matrices (resp. quasi-unitary matrices), Euclidean dual-containing (resp. Hermitian dual-containing) matrix-product codes and $q$-ary quantum codes derived from these newly constructed matrix-product codes.

•Dec 31, 2020•1 citation

A new class of self-orthogonal linear codes and their applications

Yaozong Zhang, Dabin Zheng, Xiaoqiang Wang

arXiv:2311.18432•Discrete Mathematics•Dec 8, 2025•1 citation

Three families of self-orthogonal codes and their application in optimal quantum codes

Dexiang Li, Ziling Heng, Chengju Li

Discrete Mathematics•Aug 3, 2023•12 citations
It is established in literature that finding stabilizer quantum error correcting codes (QECCS) is the same as finding self-dual additive codes over the finite field F4\mathbb{F}_{4}F4​ under the Hermitian trace inner product. Additionally, every self-dual additive code can be represented by a graph adjacency matrix. Many selfdual additive codes are constructed from circulant graphs. We introduce new graph code constructions: the Toeplitz Graph, the Multidimensional Toeplitz Graph (MDT), and the Generalized Toeplitz (GT) graph constructions. We consider some of the properties of the Toeplitz and Multidimensional Toeplitz Graphs and compare the Circulant and GT code constructions.
Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite fields. The construction of matrix-product codes with certain self-orthogonality over finite fields is an effective way to obtain good qqq-ary quantum codes of large length. Specifically, it follows from CSS construction (resp. Hermitian construction) that a matrix-product code over Fq\mathbb{F}_{q}Fq​ (resp. Fq2\mathbb{F}_{q^{2}}Fq2​) which is Euclidean dual-containing (resp. Hermitian dual-containing) can produce a qqq-ary quantum code. In order to obtain such matrix-product codes, a common way is to construct quasi-orthogonal matrices (resp. quasi-unitary matrices) as the defining matrices of matrix-product codes over Fq\mathbb{F}_{q}Fq​ (resp. Fq2\mathbb{F}_{q^{2}}Fq2​). The usage of NSC quasi-orthogonal matrices or NSC quasi-unitary matrices in this process enables the minimum distance lower bound of the corresponding quantum codes to reach its optimum. This article has two purposes: the first is to summarize some results of this topic obtained by the author of this article and his cooperators in \cite{Cao2020Constructioncaowang,Cao2020New,Cao2020Constructionof}; the second is to add some new results on quasi-orthogonal matrices (resp. quasi-unitary matrices), Euclidean dual-containing (resp. Hermitian dual-containing) matrix-product codes and qqq-ary quantum codes derived from these newly constructed matrix-product codes.