On construction of k-wise independent random variables

Abstract
A 0-1 probability space is a probabilityspace(\Omega;2\Omega; P ), where the samplespace\Omega` f0; 1gnforsome n. A probability space is k-wise independent if, when Y i is defined to be the ith coordinate ofthe random n-vector, then any subset of k of the Y i "s is (mutually) independent, and it is said tobe a probability space for p1 ; p2 ; :::; pn if P [Y i = 1] = p i .We study constructions of k-wise independent 0-1 probability spaces in which the p i "s are arbitrary.It...

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