Finite fields
Extracting randomness from samplable distributions
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Robust pcps of proximity, shorter pcps and applications to coding
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Extracting Randomness Using Few Independent Sources
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Simulating independence: new constructions of condensers, ramsey graphs, dispersers, and extractors
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Simple PCPs with poly-log rate and query complexity
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Short PCPs Verifiable in Polylogarithmic Time
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Deterministic Extractors for Affine Sources over Large Fields
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Deterministic extractors for small-space sources
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Subspace Polynomials and List Decoding of Reed-Solomon Codes
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Deterministic Extractors for Bit-Fixing Sources and Exposure-Resilient Cryptography
SIAM Journal on Computing
Deterministic Extractors for Bit-Fixing Sources by Obtaining an Independent Seed
SIAM Journal on Computing
The bit extraction problem or t-resilient functions
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Random Low Degree Polynomials are Hard to Approximate
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
From affine to two-source extractors via approximate duality
Proceedings of the forty-third annual ACM symposium on Theory of computing
On the complexity of powering in finite fields
Proceedings of the forty-third annual ACM symposium on Theory of computing
An introduction to randomness extractors
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
An elementary proof of a 3n - o(n) lower bound on the circuit complexity of affine dispersers
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Constructing high order elements through subspace polynomials
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
| Hi-index | 0.00 |
An affine disperser over F2n for sources of dimension d is a function f: F2n → F2 such that for any affine space S ⊆ F2n of dimension at least d, we have {f(s) : s in S} = F2. Affine dispersers have been considered in the context of deterministic extraction of randomness from structured sources of imperfect randomness. Previously, explicit constructions of affine dispersers were known for every d = Ω(n), due to Barak et. al.[2] and Bourgain[10] (the latter in fact gives stronger objects called affine extractors). In this work we give the first explicit affine dispersers for sublinear dimension. Specifically, our dispersers work even when d = Ω(n4/5). The main novelty in our construction lies in the method of proof, which relies on elementary properties of subspace polynomials. In contrast, the previous works mentioned above relied on sum-product theorems for finite fields.