caa a22 4500 445358785 CHVBK 20180317142908.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00493-011-2604-9 doi (NATIONALLICENCE)springer-10.1007/s00493-011-2604-9 Yehudayoff Amir Department of Mathematics, Technion — Israel Institute of Technology, 32000, Haifa, Israel aut Affine extractors over prime fields [Elektronische Daten] [Amir Yehudayoff] An affine extractor is a map that is balanced on every affine subspace of large enough dimension. We construct an explicit affine extractor AE from $\mathbb{F}^n $ to $\mathbb{F}$ , $\mathbb{F}$ a prime field, so that AE(x) is exponentially close to uniform when x is chosen uniformly at random from an arbitrary affine subspace of $\mathbb{F}^n $ of dimension at least δn, 0<δ≤1 a constant. Previously, Bourgain constructed such affine extractors when the size of $\mathbb{F}$ is two. Our construction is in the spirit of but different than Bourgain's construction. This allows for simpler analysis and better quantitative results. János Bolyai Mathematical Society and Springer Verlag, 2011 Combinatorica Springer-Verlag 31/2(2011-03-01), 245-256 0209-9683 31:2<245 2011 31 493 https://doi.org/10.1007/s00493-011-2604-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00493-011-2604-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Yehudayoff Amir Department of Mathematics, Technion — Israel Institute of Technology, 32000, Haifa, Israel aut NATIONALLICENCE 773 0- Combinatorica Springer-Verlag 31/2(2011-03-01), 245-256 0209-9683 31:2<245 2011 31 493 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer