Randomized Decoding of Gabidulin Codes Beyond the Unique Decoding Radius

Kurzfassung

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 polynomialtime Gabidulin code error-erasure decoding algorithm. This approach improves on generic rank-metric decoders by an exponential factor.