Designs, Codes and Cryptography

, Volume 65, Issue 1, pp 89–98

An excess theorem for spherical 2-designs


DOI: 10.1007/s10623-012-9677-3

Cite this article as:
Kurihara, H. Des. Codes Cryptogr. (2012) 65: 89. doi:10.1007/s10623-012-9677-3


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.


Q-polynomial association scheme Distance set Spherical design 

Mathematics Subject Classification

05E30 05B30 

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Mathematical InstituteTohoku UniversitySendaiJapan

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