Generic Decoding in the Sum-Rank Metric

We propose the first non-trivial generic decoding algorithm for codes in sum-rank metric. The new method combines ideas of well-known decoders Hamming and rank For same code parameters number errors, decoder has a larger expected complexity than known metric smaller rank-metric decoders. Furthermore, we give formal hardness reduction, providing evidence that is computationally hard. As by-product above, solve some fundamental coding problems metric: an to compute exact size sphere given radius, also upper bound as closed formula; study erasure with respect two different notions support.