Packing and Decomposition Problems for Polynomial Association Schemes

We consider P- and Q-polynomial association schemes and introduce definitions of Delsarte codes and decomposable schemes. Many known combinatorial notions can be defined as Delsarte codes in suitable association schemes, and almost all classical association schemes turn out to be decomposable. For decomposable association schemes we prove some packing bounds, which were proven before only for antipodal schemes. We also prove that any Delsarte code consists of maximal possible numbers of points for its minimal distance. Some statements about the connection between designs in decomposable schemes and designs in their projections are also given. Detailed proofs of some of our results will be published in the longer paper [24], where analogous problems for a wider class of finite and infinite polynomial metric spaces are considered.