Abstract
Let d ⩾ 2 . A construction of d-dimensional dual hyperovals in PG ( 2 d + 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 ( 2 d + 1 , 2 ) constructed from quadratic APN functions are also d-dimensional dual hyperovals in PG ( 2 d + 1 , 2 ) if, and only if, d is even. Some examples are presented.
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