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We prove that Alekhnovich's algorithm can be used for row reduction of skewpolynomial matrices. This yields an $O(\ell^3 n^{(\omega+1)/2} \log(n))$decoding algorithm for $\ell$-Interleaved Gabidulin codes of length $n$, where$\omega$ is the matrix multiplication exponent, improving in the exponent of$n$ compared to previous results.

Decoding Interleaved Gabidulin Codes using Alekhnovich's Algorithm