Unconditional proof of tightness of Johnson bound
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
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
Synopses for query optimization: A space-complexity perspective
ACM Transactions on Database Systems (TODS) - Special Issue: SIGMOD/PODS 2004
Explicit capacity-achieving list-decodable codes
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Extractors from Reed-Muller codes
Journal of Computer and System Sciences - Special issue on FOCS 2001
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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
On Hash Functions and List Decoding with Side Information
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes
Journal of the ACM (JACM)
List Decoding of Binary Codes---A Brief Survey of Some Recent Results
IWCC '09 Proceedings of the 2nd International Workshop on Coding and Cryptology
Simple extractors via constructions of cryptographic pseudo-random generators
Theoretical Computer Science
Near-optimal extractors against quantum storage
Proceedings of the forty-second ACM symposium on Theory of computing
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
Optimal error correction for computationally bounded noise
IEEE Transactions on Information Theory
A lower bound on list size for list decoding
IEEE Transactions on Information Theory
A lower bound on list size for list decoding
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
On the list decodability of random linear codes with large error rates
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Informally, an error-correcting code has "nice" list-decodability properties if every Hamming ball of "large" radius has a "small" number of codewords in it. We report linear codes with nontrivial list-decodability: i.e., codes of large rate that are nicely list-decodable, and codes of large distance that are not nicely list-decodable. Specifically, on the positive side, we show that there exist codes of rate R and block length n that have at most c codewords in every Hamming ball of radius H-1(1-R-1/c)·n. This answers the main open question from the work of Elias (1957). This result also has consequences for the construction of concatenated codes of good rate that are list decodable from a large fraction of errors, improving previous results of Guruswami and Sudan (see IEEE Trans. Inform. Theory, vol.45, p.1757-67, Sept. 1999, and Proc. 32nd ACM Symp. Theory of Computing (STOC), Portland, OR, p. 181-190, May 2000) in this vein. Specifically, for every ε > 0, we present a polynomial time constructible asymptotically good family of binary codes of rate Ω(ε4) that can be list-decoded in polynomial time from up to a fraction (1/2-ε) of errors, using lists of size O(ε-2). On the negative side, we show that for every δ and c, there exists τ < δ, c1 > 0, and an infinite family of linear codes {Ci}i such that if ni denotes the block length of Ci, then C i has minimum distance at least δ · ni and contains more than c1 · nic codewords in some Hamming ball of radius τ · ni. While this result is still far from known bounds on the list-decodability of linear codes, it is the first to bound the "radius for list-decodability by a polynomial-sized list" away from the minimum distance of the code