The Taub Faculty of Computer Science Events and Talks

The first half of the talk will overview Delsarte's association scheme-theoretic approach to coding theory, which has been used extensively over the past few decades to obtain bounds on many different classes of codes. For example, the Hamming scheme and the Johnson scheme both have classical roles in the theory of linear codes and constant-weight codes respectively, whereas the permutation scheme has been used recently in the study of permutation codes, a less well-known class of codes defined over permutations that have applications to powerline communication design. The last half of the talk will focus on a simultaneous generalization of the Johnson scheme and the permutation scheme called the injection scheme, an association scheme defined over the collection of all injective functions from a k-element set to a n-element set where k is no larger than n. Through a deeper understanding of the algebraic structure of this scheme, we are able to improve the known bounds for injection codes for various values of k and n. This is joint work with Peter Dukes and Ferdinand Ihringer. Nathan Lindzey received his Ph.D from the Department of Combinatorics and Optimization at the University of Waterloo under the supervision of Chris Godsil and Joseph Cheriyan. He is currently a postdoc under the supervision of Yuval Filmus in the Faculty of Computer Science at Technion.