Combinatorica

, 31:245 | Cite as

Affine extractors over prime fields

Article

Abstract

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.

Mathematics Subject Classification (2000)

11T23 

References

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Copyright information

© János Bolyai Mathematical Society and Springer Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsTechnion — Israel Institute of TechnologyHaifaIsrael

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