Coherent configurations and triply regular association schemes obtained from spherical designs

Details Coherent configurations and triply regular association schemes obtained from spherical designs Coherent configurations and triply regular association schemes obtained from spherical designs

2009-03-30

arxiv.org/abs/0903.5169v1

Mathematics

Combinatorics

17pages

Scientific paper

Delsarte-Goethals-Seidel showed that if $X$ is a spherical $t$-design with degree $s$ satisfying $t\geq 2s-2$, $X$ carries the structure of an association scheme. Also Bannai-Bannai showed that the same conclusion holds if $X$ is an antipodal spherical $t$-design with degree $s$ satisfying $t=2s-3$. As a generalization of these results, we prove that a union of spherical designs with a certain property carries the structure of a coherent configuration. We derive triple regularity of tight spherical $4,5,7$-designs, mutually unbiased bases, linked symmetric designs with certain parameters.

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