Coherent configurations and triply regular association schemes obtained from spherical designs

Authors:
Sho Suda
Affiliations:
Division of Mathematics, Graduated School of Information Sciences, Tohoku University, 6-3-09 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, Japan
Venue:
Journal of Combinatorial Theory Series A
Year:
2010

Citing 3
Cited 0

Matrix analysis

Matrix analysis
On Spin Models, Triply Regular Association Schemes, and Duality

Journal of Algebraic Combinatorics: An International Journal
Imprimitive cometric association schemes: Constructions and analysis

Journal of Algebraic Combinatorics: An International Journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

Delsarte, Goethals and 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 and 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 systems of symmetric designs with certain parameters.