Simple Constructions of Almost k-wise Independent Random Variables (1992)
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BibTeX
@INPROCEEDINGS{Alon92simpleconstructions,
author = {Noga Alon and Oded Goldreich and Johan Håstad and René Peralta},
title = {Simple Constructions of Almost k-wise Independent Random Variables},
booktitle = {},
year = {1992},
pages = {289--304},
publisher = {}
}
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Abstract
We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1))(log log n + k/2 + log k + log 1 ɛ), where ɛ is the statistical difference between the distribution induced on any k bit locations and the uniform distribution. This is asymptotically comparable to the construction recently presented by Naor and Naor (our size bound is better as long as ɛ < 1/(k log n)). An additional advantage of our constructions is their simplicity.
