Affine extractors over large fields with exponential error

Jean Bourgain; Zeev Dvir; Ethan Leeman

doi:10.1007/s00037-015-0108-5

Affine extractors over large fields with exponential error

Jean Bourgain, Zeev Dvir, Ethan Leeman

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

5 Scopus citations

Abstract

We describe a construction of explicit affine extractors over large finite fields with exponentially small error and linear output length. Our construction relies on a deep theorem of Deligne giving tight estimates for exponential sums over smooth varieties in high dimensions.

Original language	English (US)
Pages (from-to)	921-931
Number of pages	11
Journal	Computational Complexity
Volume	25
Issue number	4
DOIs	https://doi.org/10.1007/s00037-015-0108-5
State	Published - Dec 1 2016

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Mathematics
Computational Theory and Mathematics
Computational Mathematics

Keywords

Explicit constructions
derandomization
finite fields

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10.1007/s00037-015-0108-5

Cite this

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title = "Affine extractors over large fields with exponential error",

abstract = "We describe a construction of explicit affine extractors over large finite fields with exponentially small error and linear output length. Our construction relies on a deep theorem of Deligne giving tight estimates for exponential sums over smooth varieties in high dimensions.",

keywords = "Explicit constructions, derandomization, finite fields",

author = "Jean Bourgain and Zeev Dvir and Ethan Leeman",

note = "Publisher Copyright: {\textcopyright} 2015, Springer Basel.",

year = "2016",

month = dec,

day = "1",

doi = "10.1007/s00037-015-0108-5",

language = "English (US)",

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AU - Bourgain, Jean

AU - Dvir, Zeev

AU - Leeman, Ethan

PY - 2016/12/1

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N2 - We describe a construction of explicit affine extractors over large finite fields with exponentially small error and linear output length. Our construction relies on a deep theorem of Deligne giving tight estimates for exponential sums over smooth varieties in high dimensions.

AB - We describe a construction of explicit affine extractors over large finite fields with exponentially small error and linear output length. Our construction relies on a deep theorem of Deligne giving tight estimates for exponential sums over smooth varieties in high dimensions.

KW - Explicit constructions

KW - derandomization

KW - finite fields

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DO - 10.1007/s00037-015-0108-5

M3 - Article

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SP - 921

EP - 931

JO - Computational Complexity

JF - Computational Complexity

IS - 4

ER -

Affine extractors over large fields with exponential error

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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