Faculty Advisor

Martin, William J


A collection C of binary n-tuples is considered t-wise independent if the projection onto any t coordinates is uniformly distributed as c is chosen uniformly from C. Notice that for C to be t-wise independent, |C| must be greater than 2^t; for many applications this is too large. The aim of this project is to decrease the size of |C| while still allowing the projection onto any t coordinates to appear uniformly distributed in {0, 1}^t. In this paper I will be presenting two definitions for almost t-wise independence. Through coding theory tools I will show bounds imposed on the size of C based on those definitions. Through known constructions of almost independent binary random variables, I will then demonstrate how the definitions and bounds I established apply to these constructions.


Worcester Polytechnic Institute

Date Accepted

April 2009


Mathematical Sciences

Project Type

Major Qualifying Project



Advisor Department

Mathematical Sciences