Decoding of Reed Solomon codes beyond the error-correction bound
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List decoding algorithms for certain concatenated codes
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Bounds for Dispersers, Extractors, and Depth-Two Superconcentrators
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List decoding: algorithms and applications
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Pseudorandom generators without the XOR lemma
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Extractors and pseudorandom generators
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Linear time erasure codes with nearly optimal recovery
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Hardness of Approximating Minimization Problems
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Expander-Based Constructions of Efficiently Decodable Codes
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Extractors from Reed-Muller Codes
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Simple Extractors for All Min-Entropies and a New Pseudo-Random Generator
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
List decoding of error-correcting codes
List decoding of error-correcting codes
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
Combinatorial bounds for list decoding
IEEE Transactions on Information Theory
Guest column: error-correcting codes and expander graphs
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Correcting Errors Beyond the Guruswami-Sudan Radius in Polynomial Time
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Extractors from Reed-Muller codes
Journal of Computer and System Sciences - Special issue on FOCS 2001
Algorithmic results in list decoding
Foundations and Trends® in Theoretical Computer Science
Extractors for Three Uneven-Length Sources
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
List decoding tensor products and interleaved codes
Proceedings of the forty-first annual ACM symposium on Theory of computing
List decoding and pseudorandom constructions
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
List Decoding Tensor Products and Interleaved Codes
SIAM Journal on Computing
Reconstructive dispersers and hitting set generators
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Improving the alphabet-size in high noise, almost optimal rate list decodable codes
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
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We present an explicit construction of codes that can be list decoded from a fraction (1-ε) of errors in sub-exponential time and which have rate ε/logO(1)(1/ε). This comes close to the optimal rate of Ω(ε), and is the first sub-exponential complexity construction to beat the rate of ε2 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(ε2) rate barrier due to the 2 log (1/ε) 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(ε2) 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 from our work is perhaps conceptual, namely that good strong extractors for low min-entropies will yield near-optimal list decodable codes. Given all the progress that has been made on extractors, we view this as an optimistic avenue to look for better list decodable codes, both by looking for better explicit extractor constructions, as well as by importing non-trivial techniques from the extractor world in reasoning about and constructing codes.