  The list-decodability of random linear rank-metric codes is shown to match
that of random rank-metric codes. Specifically, an $\mathbb{F}_q$-linear
rank-metric code over $\mathbb{F}_q^{m \times n}$ of rate $R =
(1-\rho)(1-\frac{n}{m}\rho)-\varepsilon$ is shown to be (with high probability)
list-decodable up to fractional radius $\rho \in (0,1)$ with lists of size at
most $\frac{C_{\rho,q}}{\varepsilon}$, where $C_{\rho,q}$ is a constant
depending only on $\rho$ and $q$. This matches the bound for random rank-metric
codes (up to constant factors). The proof adapts the approach of Guruswami,
H\aa stad, Kopparty (STOC 2010), who established a similar result for the
Hamming metric case, to the rank-metric setting.
