Symplectic Spreads

Let pi be a semifield flock of a quadratic cone translation plane with spread in PG(3, q). In 1987, Johnson [710] showed that semifield flocks of quadratic cones, semifields of order q2 that commute over a left nucleus GF (q), are equivalent to semifields of order q2 that commute over a right or middle nucleus isomorphic to GF (q). Since semifields of order q2 that commute over a middle nucleus GF (q) are commutative, there is an implicit connection with commutative semifields of order q2 with middle nucleus GF (q) and semifield flocks.