On Unitals with Many Baer Sublines

Baer Subplanes, Ovals and Unitals

Automorphisms of Unitals

It is shown that every automorphism of classical unitals over certain (not necessarily commutative) fields is induced by a semi-similitude of a corresponding hermitian form. In particular, this is true if the form uses an involution of the second kind. In [16], J. Tits has studied classical unitals, defined by suitable polarities. Using the Borel–Tits Theorem [2], he determines the full group o...

Collineation Groups Preserving a Unital in a Projective Plane of Order

A unital embedded in a finite projective plane Π of order m# is a substructure of Π which forms a 2®(m$­1,m­1, 1) design. Several authors devoted their attention to the embedded unitals. The main aim is either to construct and investigate new classes of unitals, or to characterize some classes using group-theoretical or graphical properties [3, 6, 9, 18, 25]. In [3] we give some general results...

Classes of optical orthogonal codes from arcs in root subspaces

We present new constructions for (n, w, λ) optical orthogonal codes (OOC) using techniques from finite projective geometry. In one case codewords correspond to (q − 1)-arcs contained in Baer subspaces (and, in general, kth-root subspaces) of a projective space. In the other construction, we use sublines isomorphic to PG(1, q) lying in a projective plane isomorphic to PG(1, qk), k > 1. Our const...

Non-Existence of isomorphisms between certain unitals

We show that the Ree-Tits unitals are neither classical nor isomorphic to the polar unitals found in the Coulter-Matthews planes. To this end, we determine the full automorphism groups of the (finite) Ree unitals.