Codes usually correspond to dense packings in metric spaces and designs are a finite subsets of (possibly infinite) spaces that approximate (in a precise sense) the whole space efficiently. These concepts are in some sense dual to each other. In this project we investigate extremal combinatorial problems for codes and designs in various spaces, namely in finite classical polar spaces, finite Coxeter groups and Grassmann and Stiefel manifolds. The methods combine algebraic combinatorics, in particular association schemes, harmonic analysis and group theory.
DFG Programme
CRC/Transregios
