Generic Decoding in the Sum-Rank Metric
Abstract
We propose the first non-trivial generic decoding algorithm for codes in the sum-rank metric. The new method combines ideas of well-known generic decoders in the Hamming and rank metric. For the same code parameters and number of errors, the new generic decoder has a larger expected complexity than the known generic decoders for the Hamming metric and smaller than the known rank-metric decoders. Furthermore, we give a formal hardness reduction, providing evidence that generic sum-rank decoding is computationally hard. As a by-product of the above, we solve some fundamental coding problems in the sum-rank metric: we give an algorithm to compute the exact size of a sphere of a given sum-rank radius, and also give an upper bound as a closed formula; and we study erasure decoding with respect to two different notions of support.
Cite
@article{arxiv.2001.04812,
title = {Generic Decoding in the Sum-Rank Metric},
author = {Sven Puchinger and Julian Renner and Johan Rosenkilde},
journal= {arXiv preprint arXiv:2001.04812},
year = {2021}
}