Geometric Constructions of Codes
Dr. Keith Mellinger
University of Mary Washington

Abstract:

Finite geometry has played a role in the construction of various classes of error-correcting codes over the years, especially linear block codes. In this talk, I will discuss some recent ideas on the construction of codes using various incidence structures arising in finite projective spaces. We concentrate on three major classes of codes: low-density parity-check codes, optical orthogonal codes, and constant composition codes. The first class, LDPC codes, are well-known because of their very high performance over certain channels when coupled with certain iterative decoding techniques. The last two classes are non-linear codes used for a variety of applications involving fiber optics and electic power line transmissions. Much of this work is joint with Tim Alderson (Univ. of New Brunswick, CA) and several UMW undergraduates.