Almost k-wise independence versus k-wise independence

Noga Alon, Oded Goldreich*, Yishay Mansour

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 -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 (,k)-wise independent distributions whose statistical distance is at least nO(k)· 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)·.

Original languageEnglish
Pages (from-to)107-110
Number of pages4
JournalInformation Processing Letters
Volume88
Issue number3
DOIs
StatePublished - 15 Nov 2003

Funding

FundersFunder number
Hermann Minkowski Minerva Center for Geometry
USA Israeli BSF
Minerva Foundation
Israel Science Foundation
Tel Aviv University

    Keywords

    • Almost k-wise independent distributions
    • Combinatorial problems
    • Small probability spaces
    • Small-bias probability spaces
    • Theory of computation
    • k-wise independent distributions

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