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
Expanders that beat the eigenvalue bound: explicit construction and applications
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Pseudorandomness for network algorithms
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Computational Complexity
Journal of Computer and System Sciences
On Unapproximable Versions of NP-Complete Problems
SIAM Journal on Computing
Checking polynomial identities over any field: towards a derandomization?
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Randomness-optimal oblivious sampling
Proceedings of the workshop on Randomized algorithms and computation
Journal of Computer and System Sciences - Special issue on the 36th IEEE symposium on the foundations of computer science
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Randomness efficient identity testing of multivariate polynomials
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Extractors and pseudorandom generators
Journal of the ACM (JACM)
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
Extractors: optimal up to constant factors
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
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
Extractors from Reed-Muller Codes
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Pseudo-random generators for all hardnesses
Journal of Computer and System Sciences - STOC 2002
Deterministic Polynomial Identity Testing in Non-Commutative Models
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Simple extractors for all min-entropies and a new pseudorandom generator
Journal of the ACM (JACM)
Pseudorandom generators for low degree polynomials
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Locally decodable codes with 2 queries and polynomial identity testing for depth 3 circuits
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes
Journal of the ACM (JACM)
Hi-index | 0.00 |
A number of recent results have constructed randomness extractors and pseudorandom generators (PRGs) directly from certain error-correcting codes. The underlying construction in these results amounts to picking a random index into the codeword and outputting m consecutive symbols (the codeword is obtained from the weak random source in the case of extractors, and from a hard function in the case of PRGs). We study this construction applied to general cyclic error-correcting codes, with the goal of understanding what pseudorandom objects it can produce. We show that every cyclic code with sufficient distance yields extractors that fool all linear tests. Further, we show that every polynomial code with sufficient distance yields extractors that fool all low-degree prediction tests. These are the first results that apply to univariate (rather than multivariate) polynomial codes, hinting that Reed-Solomon codes may yield good randomness extractors. Our proof technique gives rise to a systematic way of producing unconditional PRGs against restricted classes of tests. In particular, we obtain PRGs fooling all linear tests (which amounts to a construction of ε-biased spaces), and we obtain PRGs fooling all low-degree prediction tests.