On the duals of certain d-dimensional dual hyperovals in PG(2d+1,2)

Let d⩾2. A construction of d-dimensional dual hyperovals in PG(2d+1,2) using quadratic APN functions was discovered by Yoshiara in [S. Yoshiara, Dimensional dual hyperovals associated with quadratic APN functions, Innov. Incidence Geom., in press]. In this note, we prove that the duals of the d-dimensional dual hyperovals in PG(2d+1,2) constructed from quadratic APN functions are also d-dimensional dual hyperovals in PG(2d+1,2) if, and only if, d is even. Some examples are presented.