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arXiv · 0903.5169

Coherent configurations and triply regular association schemes obtained from spherical designs

Sho Suda
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Abstract

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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Sho Suda. 2009-03-30. Coherent configurations and triply regular association schemes obtained from spherical designs. https://arxiv.org/abs/0903.5169

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