, Volume 65, Issue 1-2, pp 89-98

An excess theorem for spherical 2-designs

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Abstract

We give an excess theorem for spherical 2-designs. This theorem is a dual version of the spectral excess theorem for graphs, which gives a characterization of distance-regular graphs, among regular graphs in terms of the eigenvalues and the excess. Here we give a characterization of Q-polynomial association schemes among spherical 2-designs.

This is one of several papers published together in Designs, Codes and Cryptography on the special topic: “Geometric and Algebraic Combinatorics”.