Simple Constructions of Almost k-wise Independent Random Variables

Noga Alon, Oded Goldreich, Johan Håstad, René Peralta
1992 Random structures & algorithms (Print)  
Oded Goldreicht 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 O(loglogn+k+log $), where c is the statistical difference between of 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 constant is better as long as E < 2k/n).
more » ... additional advantage of our constructions is their simplicity. Two of our constructions are based on bit sequences which are widely believed to posses "randomness properties" and our results can be viewed as an explanation and establishment of these beliefs.
doi:10.1002/rsa.3240030308 fatcat:qoi76lbbefbhdfcslprogdg6ry