On tight sets of hyperbolic quadrics

Abstract

We prove that the parameter x of a tight set T of a hyperbolic quadric Q+(2n+1,q) of an odd rank n+1 satisfies x2+w(w−x)≡0modq+1, where w is the number of points of T in any generator of Q+(2n+1,q). As this modular equation should have an integer solution in w if such a T exists, this condition rules out roughly at least one half of all possible parameters x. It generalizes a previous result by the author and K. Metsch shown for tight sets of a hyperbolic quadric Q+(5,q) (also known as Cameron–Liebler line classes in PG(3,q)).