Discrete Mathematics and Coding Theory

Research interests in this group center around structural problems in combinatorics, and coding theory, the study of schemes for encoding data to, for example, efficiently detect errors in transmission.

Faculty

Stephen Hartke works in discrete mathematics, primarily graph theory, but also combinatorics, probability, and discrete optimization. He is interested in applications of discrete mathematics, particularly to biology and computer science.

Christine Kelley works in coding theory and applied discrete mathematics. Her focus is on the analysis and construction of graph-based codes and the relationship between the graph representation of a code and its decoding performance. While much of her work is on LDPC codes, she is also interested in applying these techniques to other codes and problems in engineering.

Jamie Radcliffe works in several areas of combinatorics, discrete mathematics and geometry. His most recent work is on reconstructibility—reconstructing a geometric object from knowledge of its smaller pieces.

Judy Walker works in algebraic coding theory. Much of her work uses techniques from number theory, algebraic geometry and graph theory. She has worked with algebraic geometric codes over rings and the relationship between weight measures on these codes and exponential sums. Currently, she studies low density parity check codes, focusing especially on their pseudocodeword structure.

Graduate Students

Nate Axvig Judy Walker

Pari Ford Jamie Radcliffe

Deanna Turk Judy Walker