Recently Efremenko showed locally-decodable codes of sub-exponential
length. That result showed that these codes can handle up to
\frac{1}{3} fraction of errors. In this paper we show that the
same codes can be locally unique-decoded from error rate
\half-\alpha for any \alpha>0 and locally list-decoded from
error rate 1-\alpha for any \alpha>0, with only a constant
number of queries and a constant alphabet size. This gives the first
sub-exponential codes that can be locally list-decoded with a
constant number of queries.

Recently Efremenko showed locally-decodable codes of sub-exponential
length. That result showed that these codes can handle up to
\frac{1}{3} fraction of errors. In this paper we show that the
same codes can be locally unique-decoded from error rate
\half-\alpha for any \alpha>0 and locally list-decoded from
error rate 1-\alpha for any \alpha>0, with only a constant
number of queries and a constant alphabet size. This gives the first
sub-exponential codes that can be locally list-decoded with a
constant number of queries.