Almost k-wise independence versus k-wise independence

We say that a distribution over {0, 1}n is ( , 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 ( , k)-wise independent distributions is how close they are to some k-wise independent distribution. We show that there exists ( , k)-wise independent distribution whose statistical distance is at least nO(k)

• Type: Journal
• Year: 2002
• Where: ECCC
• Authors: Noga Alon, Oded Goldreich, Yishay Mansour
• Keywords: -wise Independent Distribution, ECCC 2002, Independent Distribution, Uniform Distribution