Monday March 10, at 3:45 pm in Roop 103; tea at 3:30


Dr. Keith Mellinger, University of Mary Washington

Geometric Techniques in Coding Theory

ABSTRACT:   There are well-known constructions of linear codes using the techniques of finite geometry and combinatorics.  Lesser well-known are the techniques for generating non-linear codes.  In recent years, there has been a great deal of interest in constructing non-linear codes because of the wealth of application they find in wireless and Internet communication.  In this talk, I will survey some of these codes, including optical orthogonal codes and constant composition codes, and describe how one can use the techniques of finite geometry to construct and analyze these codes.  In addition, I plan to comment on my experiences working with undergraduates on projects in this area.


BIOGRAPHICAL SKETCH: Keith E. Mellinger, chair of the department of mathematics, earned a Ph.D. (2001) and M.S. (1997) in mathematics from the University of Delaware, after receiving a B.S. (1995) in mathematics from Millersville University (Pennsylvania). He also had a VIGRE post-doctoral position at the University of Illinois at Chicago. The recipient of many internal grants and a Jepson Fellowship from the University of Mary Washington, Dr. Mellinger is an MAA Project NExT fellow. In 2006, he was awarded a young investigator grant from the National Security Agency for his research in finite geometry and coding theory. He has delivered professional presentations throughout the country and in Greece, Italy, and Canada, and he has been published in such journals as Designs, Codes and Cryptography, Advances in Geometry, the SIAM Journal on Discrete Mathematics, Discrete Mathematics, Finite Fields and Their Applications, Contributions to Discrete Mathematics, the Journal of Graph Theory, and Mathematics Magazine. Dr. Mellinger has served as a referee for several research journals and is a brief/script reviewer and mathematical content consultant for CyperChase, an educational television show for children ages 8 through 11. He also teaches guitar lessons and regularly performs with a local bluegrass band. He lives with his wife and two children in downtown Fredericksburg.