Affine extractors over prime fields

Amir Yehudayoff

doi:10.1007/s00493-011-2604-9

Affine extractors over prime fields

Amir Yehudayoff

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

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 Fⁿ to F, 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 dimension at least δn, 0<δ≤1 a constant. Previously, Bourgain constructed such affine extractors when the size of two. Our construction is in the spirit of but different than Bourgain's construction. This allows for simpler analysis and better quantitative results.

Original language	English
Pages (from-to)	245-256
Number of pages	12
Journal	Combinatorica
Volume	31
Issue number	2
DOIs	https://doi.org/10.1007/s00493-011-2604-9
State	Published - Mar 2011

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Computational Mathematics

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title = "Affine extractors over prime fields",

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 Fn to F, 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 dimension at least δn, 0<δ≤1 a constant. Previously, Bourgain constructed such affine extractors when the size of two. Our construction is in the spirit of but different than Bourgain's construction. This allows for simpler analysis and better quantitative results.",

author = "Amir Yehudayoff",

note = "Funding Information: * Research partially supported by NSF grants CCF–0832797",

year = "2011",

month = mar,

doi = "10.1007/s00493-011-2604-9",

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volume = "31",

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journal = "Combinatorica",

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AU - Yehudayoff, Amir

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N2 - 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 Fn to F, 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 dimension at least δn, 0<δ≤1 a constant. Previously, Bourgain constructed such affine extractors when the size of two. Our construction is in the spirit of but different than Bourgain's construction. This allows for simpler analysis and better quantitative results.

AB - 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 Fn to F, 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 dimension at least δn, 0<δ≤1 a constant. Previously, Bourgain constructed such affine extractors when the size of two. Our construction is in the spirit of but different than Bourgain's construction. This allows for simpler analysis and better quantitative results.

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U2 - 10.1007/s00493-011-2604-9

DO - 10.1007/s00493-011-2604-9

M3 - مقالة

SN - 0209-9683

VL - 31

SP - 245

EP - 256

JO - Combinatorica

JF - Combinatorica

IS - 2

ER -

Affine extractors over prime fields

Abstract

All Science Journal Classification (ASJC) codes

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