Dimensional dual hyperovals associated with Steiner systems

In Adv. Geom. 3 (2003) 245, a class of <f>d</f>-dimensional dual hyperovals is constructed starting from a subset <f>X</f> of <f>PG(d,2)</f> with certain properties. In this paper, a criterion for <f>X</f> to provide a <f>d</f>-dimensional dual hyperoval is given in terms of some functions. Based on this, we describe such subsets, and show that there are exactly two isomorphism classes of <f>d</f>-dimensional dual hyperovals arising from those subsets and that a similar statement holds for those of the associated Steiner systems <f>S(3,4,2d+1)</f>. [Copyright &y& Elsevier]