Coherent configurations and triply regular association schemes obtained from spherical designs

2009/03/30 by Sho Suda, Suda, Sho · 2 citations
Mathematics · Materials Science · Physics and Astronomy · #Mathematical Approximation and Integration #Quasicrystal Structures and Properties #Electromagnetic Scattering and Analysis

paper · pdf · doi:10.48550/arxiv.0903.5169

Abstract

Delsarte-Goethals-Seidel showed that if X is a spherical t-design with degree s satisfying t≥ 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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• Extremal orthogonal arrays
• Existence and nonexistence of spherical 5-designs of minimal type

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