Right-hand side decoding of Gabidulin code and applications
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.
Cite
@article{arxiv.2112.07322,
title = {Right-hand side decoding of Gabidulin code and applications},
author = {Maxime Bombar and Alain Couvreur},
journal= {arXiv preprint arXiv:2112.07322},
year = {2022}
}
Comments
10 pages, Accepted at the conference WCC 2022