A d-dimensional dual arc S in PG(m, q) is called a dual hyperoval if |S| attains this upper bound: |S| = qd + qdâˆ’1 + Â· Â· Â· + q + 2. If |S| = qd + qdâˆ’1 + Â· Â· Â· + q + 2, then every point on a member ofâ€¦ (More)

A d-dimensional dual arc in PG(n, q) is a higher dimensional analogue of a dual arc in a projective plane. For every prime power q other than 2, the existence of a d-dimensional dual arc (d â‰¥ 2) inâ€¦ (More)

A nite C 3-geometry is called anomalous if it is neither a building nor the A 7-geometry. It is conjectured that no ag-transitive thick anomalous C 3-geometry exists. For a ag-transitive thickâ€¦ (More)

In [4] we have studied the semibiplanes 6e m,h = A f (S e m,h) obtained as affine expansions of the d-dimensional dual hyperovals of Yoshiara [6]. We continue that investigation here, but from aâ€¦ (More)

In Adv. Geom. 3 (2003) 245, a class of d-dimensional dual hyperovals is constructed starting from a subset X of PG(d, 2) with certain properties. In this paper, a criterion for X to provide aâ€¦ (More)

Two geometric objects, incidence graphs of semibiplanes and dimensional dual hyperovals, are respectively associated with APN and quadratic APN functions. From Proposition 2 (resp. Proposition 5),â€¦ (More)