Intersections of the Hermitian surface with irreducible quadrics in PG(3,q2), q odd

Intersections of the Hermitian Surface with Irreducible Quadrics in Even Characteristic

“…In this paper we fully extend the arguments of [1] to the case of q even. It turns out that the geometric properties being considered as well as the algebraic conditions to impose are different and more involved than those for the odd q case.…”

“…In [1], we determined the possible intersection numbers between Q and H in PG(3, q 2 ) under the assumption that q is an odd prime power and Q and H share at least one tangent plane. The same problem has been studied independently also in [6] for Q an elliptic quadric; this latter work contains also some results for q even.…”

Intersection sets, three-character multisets and associated codes

“…The problem of the intersection of the Hermitian variety H with irreducible quadrics Q having the same tangent plane at a common point P ∈ Q ∩ H has been considered in detail for r = 3 in [3,4].…”