Codes and Expansions (CodEx) Seminar
Dustin G. Mixon (The Ohio State University)
Symmetry and optimality in codes
Consider the problem of arranging a given number of points in a compact metric space so that the minimum distance is maximized. Strikingly, solutions to this coding problem often exhibit some degree of symmetry. In this talk, we investigate two different directions of this phenomenon. First, we consider projective spaces in which symmetry implies optimality (joint work with Joseph Iverson). Second, we introduce a large family of spaces in which optimality implies symmetry (joint work with Chris Cox, Emily King, and Hans Parshall). Throughout, we will pose various open problems.