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In Foundations of Computer Science (FOCS), 2010 51st Annual IEEE Symposium on (October 2010), pp. 715-722, doi:10.1109/focs.2010.88 Key: citeulike:12010314
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Efremenko showed locally-decodable codes of subexponential length that can handle close to 1/6 fraction of errors. In this paper we show that the same codes can be locally unique-decoded from error rate 1/2 - α for any α > 0 and locally list-decoded from error rate 1 - α for any α > 0, with only a constant number of queries and a constant alphabet size. This gives the first sub-exponential length codes that can be locally list-decoded with a constant number of queries.
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