Generating quasi-random sequences from semi-random sources
Journal of Computer and System Sciences
On using deterministic functions to reduce randomness in probabilistic algorithms
Information and Computation
Unbiased bits from sources of weak randomness and probabilistic communication complexity
SIAM Journal on Computing - Special issue on cryptography
Expanders, randomness, or time versus space
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
Journal of Computer and System Sciences
Journal of Computer and System Sciences
On extracting randomness from weak random sources (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Decoding of Reed Solomon codes beyond the error-correction bound
Journal of Complexity
Randomness-optimal oblivious sampling
Proceedings of the workshop on Randomized algorithms and computation
Extracting all the randomness and reducing the error in Trevisan's extractors
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Pseudorandom generators without the XOR Lemma (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Computing with Very Weak Random Sources
SIAM Journal on Computing
Extractors and pseudo-random generators with optimal seed length
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Bounds for Dispersers, Extractors, and Depth-Two Superconcentrators
SIAM Journal on Discrete Mathematics
Loss-less condensers, unbalanced expanders, and extractors
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Extractors and pseudorandom generators
Journal of the ACM (JACM)
Pseudo-random generators for all hardnesses
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Perfect information leader election in log * n+0(1) rounds
Journal of Computer and System Sciences
On the complexity of approximating the VC dimension
Journal of Computer and System Sciences - Complexity 2001
Near-Optimal Conversion of Hardness into Pseudo-Randomness
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Hardness of Approximating Minimization Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Extracting randomness via repeated condensing
FOCS '00 Proceedings of the 41st Annual 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
Better extractors for better codes?
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Combinatorial bounds for list decoding
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes
Journal of the ACM (JACM)
Hardness of Reconstructing Multivariate Polynomials over Finite Fields
SIAM Journal on Computing
An introduction to randomness extractors
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
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Finding explicit extractors is an important derandomization goal that has received a lot of attention in the past decade. Previous research has focused on two approaches, one related to hashing and the other to pseudorandom generators. A third view, regarding extractors as good error correcting codes, was noticed before. Yet, researchers had failed to build extractors directly from a good code without using other tools from pseudorandomness. We succeed in constructing an extractor directly from a Reed-Muller code. To do this, we develop a novel proof technique.Furthermore, our construction is the first to achieve degree close to linear. In contrast, the best previous constructions brought the log of the degree within a constant of optimal, which gives polynomial degree. This improvement is important for certain applications. For example, it was used [E. Mossel, C. Umans, On the complexity of approximating the VC dimension, J. Comput. System Sci. 65 (2002) 660-671] to show that approximating VC dimension to within a factor of N1-δ is AM-hard for any positive δ.