Elsevier

Information Processing Letters

Volume 88, Issue 3, 15 November 2003, Pages 107-110
Information Processing Letters

Almost k-wise independence versus k-wise independence

https://doi.org/10.1016/S0020-0190(03)00359-4Get rights and content

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 nO(k)·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 nO(k)·ε.

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1

Research supported in part by a USA Israeli BSF grant, by a grant from the Israel Science Foundation and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University.

2

Supported by the MINERVA Foundation, Germany.

3

Research supported in part by a grant from the Israel Science Foundation.

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