On the List-Decodability of Random Linear Rank-Metric Codes

10/31/2017

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by   Venkatesan Guruswami, et al.

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The list-decodability of random linear rank-metric codes is shown to match that of random rank-metric codes. Specifically, an F_q-linear rank-metric code over F_q^m × n of rate R = (1-ρ)(1-n/mρ)-ε is shown to be (with high probability) list-decodable up to fractional radius ρ∈ (0,1) with lists of size at most C_ρ,q/ε, where C_ρ,q is a constant depending only on ρ and q. This matches the bound for random rank-metric codes (up to constant factors). The proof adapts the approach of Guruswami, Hå stad, Kopparty (STOC 2010), who established a similar result for the Hamming metric case, to the rank-metric setting.