Compact Association Schemes and Fourier Analysis

Error-correcting codes are a fundamental tool in information and communication technologies. They can be viewed as collections of points in a space that are sufficiently far apart to allow error detection and correction.
More broadly, coding theory studies good arrangements of points in spaces. This theory has been particularly developed in the frameworks of association schemes and compact homogeneous spaces, where harmonic analysis plays a central role.
In this talk, we will begin with an introduction to error-correcting codes and then present compact association schemes, which we define as a generalization of these spaces in which harmonic analysis can be developed.