On symplectic semifield spreads of PG(5,q 2), q odd

Abstract

AbstractWe prove that there exist exactly three non-equivalent symplectic semifield spreads of{\operatorname{PG}(5,q^{2})}, for{q^{2}>2\cdot 3^{8}}odd, whose associated semifield has center containing{\mathbb{F}_{q}}. Equivalently, we classify, up to isotopy, commutative semifields of order{q^{6}}, for{q^{2}>2\cdot 3^{8}}odd, with middle nucleus containing{\mathbb{F}_{q^{2}}}and center containing{\mathbb{F}_{q}}.