  We give a linear-time erasure list-decoding algorithm for expander codes.
More precisely, let $r > 0$ be any integer. Given an inner code $C_0$ of length
$d$, and a $d$-regular bipartite expander graph $G$ with $n$ vertices on each
side, we give an algorithm to list-decode the expander code $C = C(G, C_0)$ of
length $nd$ from approximately $\delta \delta_r nd$ erasures in time $n \cdot
\mathrm{poly}(d2^r / \delta)$, where $\delta$ and $\delta_r$ are the relative
distance and the $r$'th generalized relative distance of $C_0$, respectively.
To the best of our knowledge, this is the first linear-time algorithm that can
list-decode expander codes from erasures beyond their (designed) distance of
approximately $\delta^2 nd$.
  To obtain our results, we show that an approach similar to that of (Hemenway
and Wootters, Information and Computation, 2018) can be used to obtain such an
erasure-list-decoding algorithm with an exponentially worse dependence of the
running time on $r$ and $\delta$; then we show how to improve the dependence of
the running time on these parameters.
