MDS codes with Galois hulls of arbitrary dimensions and the related entanglement-assisted quantum error correction

M Cao - IEEE Transactions on Information Theory, 2021 - ieeexplore.ieee.org
Let be a prime power and be an integer with. The-Galois hull of classical linear codes is a
generalization of the Euclidean hull and Hermitian hull. We provide a necessary and …

Stabilizer quantum codes from J-affine variety codes and a new Steane-like enlargement

C Galindo, F Hernando, D Ruano - Quantum Information Processing, 2015 - Springer
New stabilizer codes with parameters better than the ones available in the literature are
provided in this work, in particular quantum codes with parameters 127, 63, ≥ 12 _2 127 …

On the duals and hulls of linear codes

M Cao, J Yang, F Wei - Cryptography and Communications, 2024 - Springer
Let SLAut (F qn) denote the group of all semilinear isometries on F qn, where q= pe is a
prime power. In this paper, we investigate some general properties of linear codes …

On the distance of stabilizer quantum codes from J-affine variety codes

C Galindo, O Geil, F Hernando, D Ruano - Quantum Information …, 2017 - Springer
Self-orthogonal J-affine variety codes have been successfully used to obtain quantum
stabilizer codes with excellent parameters. In a previous paper we gave formulae for the …

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

M Cao - Finite Fields and Their Applications, 2024 - Elsevier
Matrix-product (MP) codes are a type of long codes formed by combining several
commensurate constituent codes with a defining matrix. In this paper, we study the MP code …

New binary and ternary LCD codes

C Galindo, O Geil, F Hernando… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org
LCD codes are linear codes with important cryptographic applications. Recently, a method
has been presented to transform any linear code into an LCD code with the same …

Entanglement-assisted quantum codes from matrix-product codes

X Liu, H Liu, L Yu - Quantum Information Processing, 2019 - Springer
Entanglement-assisted quantum codes are studied from classical matrix-product codes point
of view. Four methods to construct Entanglement-assisted quantum codes from matrix …

Application of Euclidean sums of matrix-product codes to quantum codes

J Liu, P Hu, X Liu - Quantum Information Processing, 2023 - Springer
It is well-known that it is an important task to construct quantum codes with good parameters.
In this paper, we first give the definition of the Euclidean sums of classical codes, and prove …

On new quantum codes from matrix product codes

X Liu, HQ Dinh, H Liu, L Yu - Cryptography and Communications, 2018 - Springer
Quantum error-correcting codes are studied from classical matrix product codes point of
view. Two methods to construct quantum codes from matrix product codes are provided …

About the generalized Hamming weights of matrix-product codes

R San-José - arXiv preprint arXiv:2407.11810, 2024 - arxiv.org
We derive a general lower bound for the generalized Hamming weights of nested matrix-
product codes, with a particular emphasis on the cases with two and three constituent codes …