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Randomized Decoding of Gabidulin Codes Beyond the Unique Decoding Radius

11/29/2019
by   Julian Renner, et al.
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We address the problem of decoding Gabidulin codes beyond their error-correcting 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 columns 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.

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