STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the complexity of approximating the VC dimension
Journal of Computer and System Sciences - Complexity 2001
Linear time encodable and list decodable codes
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Reconstructing curves in three (and higher) dimensional space from noisy data
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
European Journal of Combinatorics
Better extractors for better codes?
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Limits to list decoding Reed-Solomon codes
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Correcting Errors Beyond the Guruswami-Sudan Radius in Polynomial Time
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Explicit capacity-achieving list-decodable codes
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Algorithmic results in list decoding
Foundations and Trends® in Theoretical Computer Science
Concatenated codes can achieve list-decoding capacity
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Cryptography with constant computational overhead
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Better Binary List-Decodable Codes Via Multilevel Concatenation
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Improvements on the Johnson bound for Reed-Solomon codes
Discrete Applied Mathematics
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Better binary list decodable codes via multilevel concatenation
IEEE Transactions on Information Theory
On the list-decodability of random linear codes
Proceedings of the forty-second ACM symposium on Theory of computing
The existence of concatenated codes list-decodable up to the hamming bound
IEEE Transactions on Information Theory
Hardness amplification within NP against deterministic algorithms
Journal of Computer and System Sciences
Hardness amplification via space-efficient direct products
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
How to keep a secret: leakage deterring public-key cryptosystems
Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security
Linear-time encodable codes meeting the gilbert-varshamov bound and their cryptographic applications
Proceedings of the 5th conference on Innovations in theoretical computer science
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We present several novel constructions of codes which share the common thread of using expander (or expander-like) graphs as a component. The expanders enable the design of efficient decoding algorithms that correct a large number of errors through various forms of "voting" procedures. We consider both the notions of unique and list decoding, and in all cases obtain asymptotically good codes which are decodable up to a "maximum" possible radius and either (a) achieve a similar rate as the previously best known codes but come with significantly faster algorithms, or (b) achieve a rate better than any prior construction with similar error-correction properties. Among our main results are:Codes of rate \Omega (\varepsilon ^2 ) over constant-sized alphabet that can be list decoded in quadratic time from (1 - \varepsilon) errors. This matches the performance of the best algebraic-geometric (AG) codes, but with much faster encoding and decoding algorithms.Codes of rate \Omega(\varepsilon) over constant-sized alphabet that can be uniquely decoded from (1/2 - \varepsilon errors in near-linear time (once again this matches AG-codes with much faster algorithms). This construction is similar to that of [1], and our decoding algorithm can be viewed as a positive resolution of their main open question.Linear-time encodable and decodable binary codes of positive rate1 (in fact, rate \Omega(\varepsilon4)) that can correct up to (1/4 - \varepsilon) fraction errors. Note that this is the best error-correction one can hope for using unique decoding of binary codes. This significantly improves the fraction of errors corrected by the earlier linear-time codes of Spielman [19] and the linear-time decodable codes of [18, 22].