Affine extractors over prime fields (Q653998)

An affine extractor is a map from the \(n\)-dimensional vector space over a finite field to the field that is balanced on every affine subspace of sufficiently large dimension. Affine extractors have been studied by \textit{A.~Gabizon} and \textit{R.~Raz} [Combinatorica 28, No. 4, 415--440 (2008; Zbl 1174.05117)] for large fields and by \textit{J.~Bourgain} [Geom.\ Funct.\ Anal. 17, No. 1, 33--57 (2007; Zbl 1115.68108)] for the binary field. Here the author constructs affine extractors for any field of prime order. His construction is reminiscent to Bourgain's but different. The proof is based on bounds on certain exponential sums.