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Randomized Decoding of Gabidulin Codes Beyond the Unique Decoding Radius (1911.13193v3)
Published 29 Nov 2019 in cs.IT, cs.CR, and math.IT
Abstract: We address the problem of decoding Gabidulin codes beyond their unique error-correction radius. The complexity of this problem is of importance to assess the security of some rank-metric code-based cryptosystems. We propose an approach that introduces row or column erasures to decrease the rank of the error in order to use any proper polynomial-time Gabidulin code error-erasure decoding algorithm. This approach improves on generic rank-metric decoders by an exponential factor.