Right-hand side decoding of Gabidulin code and applications

TL;DR

This paper presents a novel right-hand side decoding algorithm for Gabidulin codes, extending previous work to non-full length codes and offering a natural approach for decoding interleaved Gabidulin codes.

Contribution

It introduces a generalized right-hand side decoding algorithm for Gabidulin codes, applicable to non-full length codes and enhances decoding of interleaved Gabidulin codes.

Findings

Decoding algorithm acts on codewords on the right, differing from traditional left-action methods.

The generalized algorithm applies to non-full length Gabidulin codes.

Provides a clear and natural approach for decoding interleaved Gabidulin codes.

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.