Abstract
By [4] a doubly transitive, non-solvable dimensional dual hyperoval D is isomorphic either to the Mathieu dual hyperoval or to a quotient of a Huybrechts dual hyperoval. In order to determine all doubly transitive dimensional dual hyperovals, it remains to classify the solvable ones, and this paper is a contribution to this problem. A doubly transitive, solvable dimensional dual hyperoval D of rank n is defined over 𝔽2 and has an automorphism of the form ES, where E is elementary abelian of order 2n and S ≤ Γ L(1, 2n); see Yoshiara [12]. The known examples D are bilinear. In [1] the bilinear, doubly transitive, solvable dimensional dual hyperovals D of rank n with GL(1, 2n) ≤ S are classified. Here we present two new classes of non-bilinear, doubly transitive dimensional dual hyperovals. We also consider universal covers of doubly transitive dimensional dual hyperovals, since they are again doubly transitive dimensional dual hyperovals by [2, Cor. 1.3]. We determine the universal covers of the presently known doubly transitive dimensional dual hyperovals.