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Maximum-Likelihood Decoding of Gabidulin Codes Is NP-Hard Even in Dimension One
Fix a prime power q. We prove that deciding whether a received word y in Fnqm lies at rank distance at most n-2 from the one-dimensional Gabidulin code {{λ.g : λ in Fqm } is NP-complete. Thus maximum-likelihood decoding of Gabidulin codes is NP-hard even for k = 1, an analogue of the Guruswami-Vardy
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