Deterministic extractors for affine sources over large fields
نویسندگان
چکیده
منابع مشابه
Deterministic Extractors for Algebraic Sources
An algebraic source is a random variable distributed uniformly over the set of common zeros of one or more multivariate polynomials defined over a finite field F. Our main result is the construction of an explicit deterministic extractor for algebraic sources over exponentially large prime fields. More precisely, we give an explicit (and arguably simple) function E : Fn 7→ {0, 1}m such that the...
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We propose a new model of a weakly random source that admits randomness extraction. Our model of additive sources includes such natural sources as uniform distributions on arithmetic progressions (APs), generalized arithmetic progressions (GAPs), and Bohr sets, each of which generalizes affine sources. We give an explicit extractor for additive sources with linear minentropy over both Zp and Z ...
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We give the first explicit construction of deterministic extractors for affine sources over F2, with entropy k ≥ log n for some large enough constant C, where n is the length of the source. Previously the best known results are by Bourgain [Bou07], Yehudayoff [Yeh11] and Li [Li11b], which require the affine source to have entropy at least Ω(n/ √ log log n). Our extractor outputs one bit with er...
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A polynomial source of randomness over Fq is a random variable X = f (Z) where f is a polynomial map and Z is a random variable distributed uniformly over Fq for some integer r. The three main parameters of interest associated with a polynomial source are the order q of the field, the (total) degree D of the map f , and the base-q logarithm of the size of the range of f over inputs in Fq, denot...
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2008
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-008-2259-3