Galois hulls of linear codes over finite fields

H Liu, X Pan - Designs, Codes and Cryptography, 2020 - Springer
The ℓ ℓ-Galois hull h_ ℓ (C) h ℓ (C) of an n, k linear code C over the finite field F _q F q is the
intersection of C and C^\bot _ ℓ C⊥ ℓ, where C^\bot _ ℓ C⊥ ℓ denotes the ℓ ℓ-Galois dual of …

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 …

Matrix product codes over finite commutative Frobenius rings

Y Fan, S Ling, H Liu - Designs, codes and cryptography, 2014 - Springer
Abstract Properties of matrix product codes over finite commutative Frobenius rings are
investigated. The minimum distance of matrix product codes constructed with several types …

[HTML][HTML] New quantum codes from evaluation and matrix-product codes

C Galindo, F Hernando, D Ruano - Finite Fields and Their Applications, 2015 - Elsevier
Stabilizer codes obtained via the CSS code construction and the Steane's enlargement of
subfield-subcodes and matrix-product codes coming from generalized Reed–Muller …

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 …

[HTML][HTML] On matrix-product structure of repeated-root constacyclic codes over finite fields

Y Cao, Y Cao, HQ Dinh, FW Fu, P Maneejuk - Discrete Mathematics, 2020 - Elsevier
For any prime number p, positive integers m, k, n, where n satisfies gcd (p, n)= 1, and for any
non-zero element λ 0 of the finite field F pm of cardinality pm, we prove that any λ 0 p k …

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 …

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

M Cao, J Cui - Quantum Information Processing, 2020 - Springer
Abstract In 2001, Blackmore and Norton introduced an important tool called matrix-product
codes, which turn out to be very useful to construct new quantum codes of large lengths. To …

Secure and Compact: A New Variant of McEliece Cryptosystem

E Bindal, AK Singh - IEEE Access, 2024 - ieeexplore.ieee.org
This paper introduces a variant of the McEliece cryptosystem and employs the-construction
to generate a new code from two arbitrary linear codes. We propose an efficient hard …

Locally recoverable codes from the matrix-product construction

C Galindo, F Hernando, C Munuera… - arXiv preprint arXiv …, 2023 - arxiv.org
Matrix-product constructions giving rise to locally recoverable codes are considered, both
the classical $ r $ and $(r,\delta) $ localities. We study the recovery advantages offered by …