
Rod Gow

Michel Lavrauw

John Sheekey

Frédéric Vanhove
Keywords:
(partial) spread, hermitian variety, hermitian matrix, rankdistance
Abstract
In this paper we investigate partial spreads of $H(2n1,q^2)$ through the related notion of partial spread sets of hermitian matrices, and the more general notion of constant rankdistance sets. We prove a tight upper bound on the maximum size of a linear constant rankdistance set of hermitian matrices over finite fields, and as a consequence prove the maximality of extensions of symplectic semifield spreads as partial spreads of $H(2n1,q^2)$. We prove upper bounds for constant rankdistance sets for even rank, construct large examples of these, and construct maximal partial spreads of $H(3,q^2)$ for a range of sizes.