Decoding Rank Metric Reed–Muller Codes

Alain Couvreur; Rakhi Pratihar

doi:10.1109/TIT.2025.3638021

Decoding Rank Metric Reed–Muller Codes

Alain Couvreur
, Rakhi Pratihar

Laboratoire d'Informatique (LIX)

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

In this article, we investigate the decoding of the rank metric Reed–Muller codes introduced by Augot, Couvreur, Lavauzelle and Neri in 2021. These codes are defined from Abelian Galois extensions extending the construction of Gabidulin codes over arbitrary cyclic Galois extensions. We propose a polynomial time algorithm that rests on the structure of Dickson matrices, works on any such code and corrects any error of rank up to half the minimum distance.

langue originale	Anglais
Pages (de - à)	1011-1029
Nombre de pages	19
journal	IEEE Transactions on Information Theory
Volume	72
Numéro de publication	2
Les DOIs	https://doi.org/10.1109/TIT.2025.3638021
état	Publié - 1 janv. 2026

Accès au document

10.1109/TIT.2025.3638021

Autres fichiers et liens

Lien vers la publication dans Scopus

Contient cette citation

@article{18c7248b5ea34b3bb339057125d60991,

title = "Decoding Rank Metric Reed–Muller Codes",

abstract = "In this article, we investigate the decoding of the rank metric Reed–Muller codes introduced by Augot, Couvreur, Lavauzelle and Neri in 2021. These codes are defined from Abelian Galois extensions extending the construction of Gabidulin codes over arbitrary cyclic Galois extensions. We propose a polynomial time algorithm that rests on the structure of Dickson matrices, works on any such code and corrects any error of rank up to half the minimum distance.",

keywords = "Dickson matrices, Rank–metric codes, decoding algorithms",

author = "Alain Couvreur and Rakhi Pratihar",

note = "Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2026",

month = jan,

day = "1",

doi = "10.1109/TIT.2025.3638021",

language = "English",

volume = "72",

pages = "1011--1029",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

number = "2",

}

TY - JOUR

T1 - Decoding Rank Metric Reed–Muller Codes

AU - Couvreur, Alain

AU - Pratihar, Rakhi

PY - 2026/1/1

Y1 - 2026/1/1

N2 - In this article, we investigate the decoding of the rank metric Reed–Muller codes introduced by Augot, Couvreur, Lavauzelle and Neri in 2021. These codes are defined from Abelian Galois extensions extending the construction of Gabidulin codes over arbitrary cyclic Galois extensions. We propose a polynomial time algorithm that rests on the structure of Dickson matrices, works on any such code and corrects any error of rank up to half the minimum distance.

AB - In this article, we investigate the decoding of the rank metric Reed–Muller codes introduced by Augot, Couvreur, Lavauzelle and Neri in 2021. These codes are defined from Abelian Galois extensions extending the construction of Gabidulin codes over arbitrary cyclic Galois extensions. We propose a polynomial time algorithm that rests on the structure of Dickson matrices, works on any such code and corrects any error of rank up to half the minimum distance.

KW - Dickson matrices

KW - Rank–metric codes

KW - decoding algorithms

UR - https://www.scopus.com/pages/publications/105023464856

U2 - 10.1109/TIT.2025.3638021

DO - 10.1109/TIT.2025.3638021

M3 - Article

AN - SCOPUS:105023464856

SN - 0018-9448

VL - 72

SP - 1011

EP - 1029

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 2

ER -

Decoding Rank Metric Reed–Muller Codes

Résumé

Accès au document

Autres fichiers et liens

Empreinte digitale

Contient cette citation