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Penttila and Williford constructed a $4-$class association scheme from ageneralized quadrangle with a doubly subtended subquadrangle. We show that anassociation scheme with appropriate parameters and satisfying some assumptionabout maximal cliques must be the Penttila-Williford scheme.

Reconstructing a generalized quadrangle from the Penttila-Williford $4-$class association scheme