This article is about finite commutative semifields that are of rank 2 over their middle nucleus, the largest subset of elements that is a finite field. These semifields have a direct correspondence to certain flocks of the quadratic cone in
PG(3, q) and to certain ovoids of the parabolic space Q(4, q). We shall consider
these links, the known examples and non-existence results.
Ball, S.; Lavrauw, M. Commutative semifields of rank 2 over their middle nucleus. A: Finite Fields and Applications. "Finite fields with applications to coding theory, cryptography and related areas". Oaxaca: Springer, 2001, p. 1-21.