On Quasi-Hermitian Varieties in Even Characteristic and Related Orthogonal Arrays

Abstract

In this article, we study the BM quasi-Hermitian varieties, laying in the three-dimensional Desarguesian projective space of even order. After a brief investigation of their combinatorial properties, we first show that all of these varieties are projectively equivalent, exhibiting a behavior which is strikingly different from what happens in odd characteristic. This completes the classification project started there. Here we prove more; indeed, by using previous results, we explicitly determine the structure of the full collineation group stabilizing these varieties. Finally, as a byproduct of our investigation, we also construct a family of simple orthogonal arrays (Formula presented.), with entries in (Formula presented.), where (Formula presented.) is an even prime power. Orthogonal arrays (OA's) are principally used to minimize the number of experiments needed to investigate how variables in testing interact with each other.