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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.

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Authors and Affiliations

  1. Mathematical Institute, Tohoku University, Aramaki-Aza-Aoba 6-3, Aoba-ku, Sendai, 980-8578, Japan

    Hirotake Kurihara

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  1. Hirotake Kurihara
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Correspondence to Hirotake Kurihara.

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

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Kurihara, H. An excess theorem for spherical 2-designs. Des. Codes Cryptogr. 65, 89–98 (2012). https://doi.org/10.1007/s10623-012-9677-3

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  • DOI: https://doi.org/10.1007/s10623-012-9677-3

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