On the List-Decodability of Random Linear Rank-Metric Codes
On the List-Decodability of Random Linear Rank-Metric Codes
The list-decodability of random linear rank-metric codes is shown to match that of random rank-metric codes. Specifically, an F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> -linear rank-metric code over F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m×n</sup> of rate R=(1-ρ)(1-[n/m]ρ)-ε is shown to be (with high probability) list-decodable up to fractional radius ρ ∈ …