2 research outputs found
A characterization of Hermitian varieties as codewords
It is known that the Hermitian varieties are codewords in the code defined by
the points and hyperplanes of the projective spaces . In finite
geometry, also quasi-Hermitian varieties are defined. These are sets of points
of of the same size as a non-singular Hermitian variety of
, having the same intersection sizes with the hyperplanes of
. In the planar case, this reduces to the definition of a unital. A
famous result of Blokhuis, Brouwer, and Wilbrink states that every unital in
the code of the points and lines of is a Hermitian curve. We prove
a similar result for the quasi-Hermitian varieties in , ,
as well as in , prime, or , prime, and