Hermitian unitals are code words

Hermitian unitals are code words

We show that a unital in PG(2, q) is Hermitian if and only if it is in the code generated by the lines of PG(2, q). This implies the truth of a conjecture made by Assmus and Key.

Buekenhout unitals

Hermitian Function Fields, Classical Unitals, and Representations of 3-dimensional Unitary Groups

We determine the elementary divisors, and hence the rank over an arbitrary field, of the incidence matrix of the classical unital.

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.