Local List Decoding 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.