Constructions of tight sets of the Hermitian polar space $\mc{H}(2r-1,q^2)$

Abstract

In this paper, we construct two infinite families of tight sets with parameters (q 2r−2 − 1) and (q 2r−1 − q 2r−2 ), respectively, in the Hermitian polar space H(2r − 1, q 2 ) for any r ≥ 2 and any prime power q. Both families admit (q − 1).PGL(r, q 2 ).2.2e as the full automorphism group, where q = p e , p is a prime, and e a positive integer.