Unitals of PG(2,q2) Containing Conics

Intersections of Nonclassical Unitals and Conics in PG(2,q2)

In PG(2, q2) with q > 2, we determine the possible intersections of a nonclassical Buekenhout–Metz unital U and a conic passing through the point at infinity of U .

Buekenhout unitals

Unitals and codes

A program is outlined for the enumeration of unital 2-(28,4,1) designs that uses tactical decompositions de1ned by vectors of certain weight in the dual binary code of a design. A class of designs with a spread that covers a codeword of weight 12 is studied in detail. A total of 909 nonisomorphic designs are constructed that include the classical hermitian and Ree unitals, as well as many other...

Enumeration of orthogonal Buekenhout unitals

In this paper we develop general techniques for enumerating orthogonal Buekenhout unitals embedded in two-dimensional translation planes. We then apply these techniques in the regular nearfield planes, the odd-order Hall planes, and the odd-order flag-transitive affine planes. Stabilizers of the resulting unitals also are computed.

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...