  We show that expander codes, when properly instantiated, are high-rate list
recoverable codes with linear-time list recovery algorithms. List recoverable
codes have been useful recently in constructing efficiently list-decodable
codes, as well as explicit constructions of matrices for compressive sensing
and group testing. Previous list recoverable codes with linear-time decoding
algorithms have all had rate at most 1/2; in contrast, our codes can have rate
$1 - \epsilon$ for any $\epsilon > 0$. We can plug our high-rate codes into a
construction of Meir (2014) to obtain linear-time list recoverable codes of
arbitrary rates, which approach the optimal trade-off between the number of
non-trivial lists provided and the rate of the code. While list-recovery is
interesting on its own, our primary motivation is applications to
list-decoding. A slight strengthening of our result would implies linear-time
and optimally list-decodable codes for all rates, and our work is a step in the
direction of solving this important problem.
