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)

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1011-1029
Number of pages	19
Journal	IEEE Transactions on Information Theory
Volume	72
Issue number	2
DOIs	https://doi.org/10.1109/TIT.2025.3638021
Publication status	Published - 1 Jan 2026

Keywords

Dickson matrices
Rank–metric codes
decoding algorithms

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10.1109/TIT.2025.3638021

Cite this

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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.",

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KW - decoding algorithms

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Decoding Rank Metric Reed–Muller Codes

Abstract

Keywords

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