Semi-Boolean Steiner quadruple systems and dimensional dual hyperovals
نویسندگان
چکیده
A dimensional dual hyperoval satisfying property (H) [6] in a project!ve space of order 2 is naturally associated with a "semi-Boolean" Steiner quadruple system. The only known examples are associated with Boolean systems. For every d > 2, we construct a new ddimensional dual hyperoval satisfying property (H) in PG(d(d + 3)/2,2); its related semiBoolean system is the Teirlinck one. It is universal and admits quotients in PG(«,2), with 4d < n < d(d + 3)/2, if d ^ 6. We also prove the uniqueness of ^-dimensional dual hyperovals satisfying property (H) in PG(d(d + 3)/2,2), whose related semi-Boolean systems belongs to a particular class, which includes Boolean and Teirlinck systems. Finally, we prove property (ml) [6] for them.
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