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Right-hand side decoding of Gabidulin codes and applications


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.
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Dates and versions

hal-03481406 , version 1 (15-12-2021)
hal-03481406 , version 2 (07-03-2022)



Maxime Bombar, Alain Couvreur. Right-hand side decoding of Gabidulin codes and applications. WCC 2022 : The Twelfth International Workshop on Coding and Cryptography, Mar 2022, Rostock, Germany. ⟨hal-03481406v2⟩
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