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Deterministic Extractors for Affine Sources over Large Fields
[chapter]

2010
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Monographs in Theoretical Computer Science. An EATCS Series
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An (n, k)-affine source over a finite field F is a random variable X = (X 1 , ..., X n ) ∈ F n , which is uniformly distributed over an (unknown) k-dimensional affine subspace of F n . We show how to (deterministically) extract practically all the randomness from affine sources, for any field of size larger than n c (where c is a large enough constant). Our main results are as follows: 1. (For arbitrary k): For any n, k and any F of size larger than n 20 , we give an explicit construction for a

doi:10.1007/978-3-642-14903-0_3
fatcat:vhndowpghrhq3inel3dquoif5u