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.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Houde, Matthew Thomas

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-042709-214204

Advisor

• Martin, William J.

Year

• 2009

Date created

• 2009-04-27

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Rights statement

• In Copyright

Last modified

• 2021-01-06