Right-hand side decoding of Gabidulin code and applications
This work addresses decoding challenges in coding theory, particularly for Gabidulin codes, but appears incremental as it builds on existing algorithms with modifications.
The paper tackles the decoding problem for Gabidulin and interleaved Gabidulin codes by presenting a right-hand side decoding algorithm, which generalizes a previous version to handle non-full length codes and provides a clear approach for interleaved codes.
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.