Simple constructions of almost k-wise independent random variables

Noga Alon*, Oded Goldreich, Johan Hastad, Rene Peralta

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

92 Scopus citations


The authors 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 O(log log n + k + log 1/ε), where ε 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 J. Naor and M. Naor (1990). An advantage of the present constructions is their simplicity. Two of the constructions are based on bit sequences that are widely believed to possess randomness properties, and the results can be viewed as an explanation and establishment of these beliefs.

Original languageEnglish
Pages (from-to)544-553
Number of pages10
JournalAnnual Symposium on Foundations of Computer Science - Proceedings
StatePublished - 1990
EventProceedings of the 31st Annual Symposium on Foundations of Computer Science - St. Louis, MO, USA
Duration: 22 Oct 199024 Oct 1990


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