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

Quantum Information Processing

Construction of new quantum codes via Hermitian dual-containing matrix-product codes

Meng Cao, Jianlian Cui

Published Nov 24, 2020• 14 citations
Publisher
DOI
10.1007/s11128-020-02921-0

Related papers

New quantum codes from Hermitian dual-containing matrix-product codes

Jie Liu, Xiusheng Liu

Quantum Information Processing•Jul 19, 2024•4 citations

On dual-containing, almost dual-containing matrix-product codes and related quantum codes

Meng Cao

Finite Fields and Their Applications•Mar 13, 2024•5 citations

Hermitian dual-containing constacyclic BCH codes of new length and related quantum codes

Xueting Wang, Junling Zhou

Quantum Information Processing•Mar 3, 2026•0 citations

Construction of New Matrix-Product Codes and Their Applications

Hao Song, Ruihu Li, Junli Wang +1 more

In this paper, from special code chains$\mathcal {C}_{1} \supseteq \mathcal {C}_{2}~\supseteq \mathcal {C}_{3}$such that$\mathcal {C}^{\bot _{h}}_{1}\subseteq \mathcal {C}_{3}$and$\mathcal {C}^{\bot _{h}}_{2}\subseteq \mathcal {C}_{2}$, some Hermitian dual-containing (HDC) matrix-product (MP) codes are presented, where$\mathcal {C}_{3}$is not HDC. By studying some constacyclic codes of lengths$n=q^{2}\pm 1$and$n=\frac {q^{2}-1}{2}$, we construct many HDC MP codes of length$3n$. Consequently, many$q$-ary quantum codes with larger designed distance$d\geq q+1$are obtained from these MP codes, where$4\leq q\leq 9$.

IEEE Access•Jan 1, 2019•3 citations

On new quantum codes from matrix product codes

Xiusheng Liu, Hai Quang Dinh, Hualu Liu +1 more

arXiv:1604.05823•Cryptography and Communications•Jul 14, 2017•31 citations

Special matrices over finite fields and their applications to quantum error-correcting codes

Cao, Meng

The matrix-product (MP) code $\mathcal{C}_{A,k}:=[\mathcal{C}_{1},\mathcal{C}_{2},\ldots,\mathcal{C}_{k}]\cdot A$ with a non-singular by column (NSC) matrix $A$ plays an important role in constructing good quantum error-correcting codes. In this paper, we study the MP code when the defining matrix $A$ satisfies the condition that $AA^†$ is $(D,τ)$-monomial. We give an explicit formula for calculating the dimension of the Hermitian hull of a MP code. We provide the necessary and sufficient conditions that a MP code is Hermitian dual-containing (HDC), almost Hermitian dual-containing (AHDC), Hermitian self-orthogonal (HSO), almost Hermitian self-orthogonal (AHSO), and Hermitian LCD, respectively. We theoretically determine the number of all possible ways involving the relationships among the constituent codes to yield a MP code with these properties, respectively. We give alternative necessary and sufficient conditions for a MP code to be AHDC and AHSO, respectively, and show several cases where a MP code is not AHDC or AHSO. We provide the construction methods of HDC and AHDC MP codes, including those with optimal minimum distance lower bounds.

arXiv:2405.02285•May 3, 2024•0 citations
In this paper, from special code chainsC1⊇C2 ⊇C3\mathcal {C}_{1} \supseteq \mathcal {C}_{2}~\supseteq \mathcal {C}_{3}C1​⊇C2​ ⊇C3​such thatC1⊥h⊆C3\mathcal {C}^{\bot _{h}}_{1}\subseteq \mathcal {C}_{3}C1⊥h​​⊆C3​andC2⊥h⊆C2\mathcal {C}^{\bot _{h}}_{2}\subseteq \mathcal {C}_{2}C2⊥h​​⊆C2​, some Hermitian dual-containing (HDC) matrix-product (MP) codes are presented, whereC3\mathcal {C}_{3}C3​is not HDC. By studying some constacyclic codes of lengthsn=q2±1n=q^{2}\pm 1n=q2±1andn=q2−12n=\frac {q^{2}-1}{2}n=2q2−1​, we construct many HDC MP codes of length3n3n3n. Consequently, manyqqq-ary quantum codes with larger designed distanced≥q+1d\geq q+1d≥q+1are obtained from these MP codes, where4≤q≤94\leq q\leq 94≤q≤9.
The matrix-product (MP) code CA,k:=[C1,C2,…,Ck]⋅A\mathcal{C}_{A,k}:=[\mathcal{C}_{1},\mathcal{C}_{2},\ldots,\mathcal{C}_{k}]\cdot ACA,k​:=[C1​,C2​,…,Ck​]⋅A with a non-singular by column (NSC) matrix AAA plays an important role in constructing good quantum error-correcting codes. In this paper, we study the MP code when the defining matrix AAA satisfies the condition that AA†AA^†AA† is (D,τ)(D,τ)(D,τ)-monomial. We give an explicit formula for calculating the dimension of the Hermitian hull of a MP code. We provide the necessary and sufficient conditions that a MP code is Hermitian dual-containing (HDC), almost Hermitian dual-containing (AHDC), Hermitian self-orthogonal (HSO), almost Hermitian self-orthogonal (AHSO), and Hermitian LCD, respectively. We theoretically determine the number of all possible ways involving the relationships among the constituent codes to yield a MP code with these properties, respectively. We give alternative necessary and sufficient conditions for a MP code to be AHDC and AHSO, respectively, and show several cases where a MP code is not AHDC or AHSO. We provide the construction methods of HDC and AHDC MP codes, including those with optimal minimum distance lower bounds.