Corruption and Recovery-Efficient Locally Decodable Codes

A (q, , )-locally decodable code (LDC) C : {0, 1}n {0, 1}m is an encoding from n-bit strings to m-bit strings such that each bit xk can be recovered with probability at least 1 2 + from C(x) by a randomized algorithm that queries only q positions of C(x), even if up to m positions of C(x) are corrupted. If C is a linear map, then the LDC is linear. We give improved constructions of LDCs in terms of the corruption parameter and recovery parameter . The key property of our LDCs is that they are non-linear, whereas all previous LDCs were linear.

• Type: Conference
• Year: 2008
• Where: APPROX
• Authors: David P. Woodruff
• Keywords: Algorithms, APPROX 2008, Bit Xk, M-bit Strings, N-bit Strings