On a New Family of Flag-transitive Semibiplanes

Each of the d-dimensional dual hyperovals Sh m discovered by Yoshiara [20] gives rise, via affine expansion, to a flag-transitive semibiplane A f (Sh m ). We prove that, if m + h = d + 1, then A f (Sh m ) is an elation semibiplane. In the other cases, if d > 2 then A f (Sh m ) is not isomorphic to any of the examples we are aware of, except possibly for certain semibiplanes obtained from Dn -buildings defined over G F(2). However, many semibiplanes live hidden as quotients inside halved hypercubes. It is thus quite natural to ask whether any of our semibiplanes are like that. We prove that A f (Sh m ) is a quotient of a halved hypercube if and only if h = m.