Work

Right-hand side decoding of Gabidulin code and applications

Year: 2021

Type: preprint

Abstract: We discuss the decoding of Gabidulin and interleaved Gabidulin codes. We give the full presentation of a decoding algorithm for Gabidulin codes, which as Loidreau's seminal algorithm consists in localizing errors in the spirit of Berlekamp-Welch algorithm for Reed-Solomon codes. On the other hand, this algorithm consists in acting on codewords on the right while Loidreau's algorithm considers an action on the left. This right-hand side decoder was already introduced by the authors in a previous work for cryptanalytic applications. We give here a generalised version which applies to the case of non-full length Gabidulin codes. Finally, we show that this algorithm turns out to provide a very clear and natural approach for the decoding of interleaved Gabidulin codes.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2112.07322

Authors: Bombar, Maxime, Couvreur, Alain

Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, École Polytechnique, Laboratoire d'Informatique de l'École Polytechnique, Institut Polytechnique de Paris

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4226479208

Cites:

Cited by: 1

Related to: 10