Title page for E-project-042709-214204

Project Type	MQP
Submission date	2009-04-27
Author	Matthew Thomas Houde, MA
URN	E-project-042709-214204
Title	Almost Independent Binary Random Variables
Advisor	Martin, William J, MA
Availability	unrestricted
Abstract 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.
Files	Almost_Independent_Binary_Random_Variables.pdf There is one file which has been withheld at the advisor's request.

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