article

Almost k-wise independence versus k-wise independence

Authors:

Noga Alon,

Oded Goldreich,

Yishay MansourAuthors Info & Claims

Information Processing Letters, Volume 88, Issue 3

Pages 107 - 110

https://doi.org/10.1016/S0020-0190(03)00359-4

Published: 15 November 2003 Publication History

Abstract

We say that a distribution over {0,1}ⁿ is (ε,k)-wise independent if its restriction to every k coordinates results in a distribution that is ε-close to the uniform distribution. A natural question regarding (ε, k)-wise independent distributions is how close they are to some k-wise independent distribution. We show that there exist (ε, k)-wise independent distributions whose statistical distance is at least n^O(k) ċ ε from any k-wise independent distribution. In addition, we show that for any (ε,k)-wise independent distribution there exists some k-wise independent distribution, whose statistical distance is n^O(k) ċ ε.

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Information Processing Letters Volume 88, Issue 3

15 November 2003

50 pages

ISSN:0020-0190

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Elsevier North-Holland, Inc.

United States

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Published: 15 November 2003

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