Decoding Interleaved Gabidulin Codes using Alekhnovich's Algorithm

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

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