Towards 3-query locally decodable codes of subexponential length - Yekhanin, Sergey (Journal of the ACM, 2007)
A q query Locally Decodable Code (LDC) encodes an n-bit message x as an N-bit codeword C(x), such that one can probabilistically recover any bit xi of the message by querying only q bits of the codeword C(x), even after some constant fraction of codeword bits has been corrupted.