Decoding rank metric Reed-Muller codes
Alain Couvreur, Rakhi Pratihar
TL;DR
This paper presents a polynomial-time decoding algorithm for rank metric Reed-Muller codes, leveraging Dickson matrix structures to correct errors up to half the minimum distance, advancing error correction capabilities in this code class.
Contribution
It introduces a novel polynomial-time decoding algorithm for rank metric Reed-Muller codes based on Dickson matrices, applicable to codes from Abelian Galois extensions.
Findings
Decoding algorithm corrects errors up to half the minimum distance
Algorithm is applicable to codes from arbitrary cyclic Galois extensions
Decoding complexity is polynomial time
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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