Abstract
We determine all hyperplanes of DW ( 2 n - 1 , q ) , q ≠ 2 , without ovoidal quads. We will show that each such hyperplane either consists of all maximal singular subspaces of W ( 2 n - 1 , q ) which meet a given ( n - 1 ) -dimensional subspace of PG ( 2 n - 1 , q ) or (only when q is even) arises from the spin-embedding of DW ( 2 n - 1 , q ) .
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