Relaxed Locally Correctable Codes in Computationally Bounded Channels

Error-correcting codes that admit local decoding and correcting algorithms have been the focus of much recent research due to their numerous applications. An important goal is obtain best possible tradeoffs between number symbols codeword algorithm must examine (the locality), amount redundancy in encoding information rate). In Hamming's classical adversarial channel model, current are dramatic, allowing either small locality but superpolynomial blocklength, or blocklength high locality. However, computationally bounded proposed by Lipton (STACS 1994), constructions locally decodable suddenly exhibit these require strong trusted setup assumptions. We study variants correctable bounded, channels, a setting with no setup. The only assumption we selection public parameters (seed) for collision-resistant hash function. Specifically, provide relaxed over binary alphabet, constant rate, poly-logarithmic Our constructions, which compare favorably analogs, crucially employ functions expander graphs, extending ideas from cryptographic memory-hard functions.