Splitness of the Veronesean and the Taniguchi dual hyperovals

Abstract The Veronesean and the Taniguchi dual hyperovals are shown to be of split type, by constructing some symmetric bilinear maps in criterion for splitness. For the Veronesean dual hyperovals, such maps correspond to commutative presemifields in characteristic 2. For the Taniguchi dual hyperovals, their automorphism groups are determined and their actions on such maps are investigated.