Better extractors for better codes?

We present an explicit construction of codes that can be list decoded from a fraction (1 - ) of errors in sub-exponential time and which have rate / logO(1) (1/). This comes close to the optimal rate of (), and is the first sub-exponential complexity construction to beat the rate of 2 achieved by Reed-Solomon or algebraic-geometric codes. Our construction is based on recent extractor constructions with very good seed length [17]. While the "standard" way of viewing extractors as codes (as in [16]) cannot beat the O(2 ) rate barrier due to the 2 log(1/) lower bound on seed length for extractors, we use such extractor codes as a component in a well-known expander-based construction scheme to get our result. The O(2 ) rate barrier also arises if one argues about list decoding using the minimum distance (via the so-called Johnson bound) -- so this also gives the first explicit construction that "beats the Johnson bound" for list decoding from errors. The main message f...

• Type: Conference
• Year: 2004
• Where: STOC
• Authors: Venkatesan Guruswami
• Keywords: Algorithms, Explicit Extractor Constructions, Extractor Codes, List Decodable Codes, STOC 2004