KAPPA-ARCS AND PARTIAL FLOCKS

Using the relationship between partial flocks of the quadratic cone K in PG(3, q), q even, and arcs in the plane PG(2, q), new results on pa rtial flocks and short proofs for known theorems on translation genera lized quadrangles of order (q(2), q) and on ovoids in PC(3, q) are obt ained. It is shown that large partial flocks of K containing approxima tely q conics, q even, are always extendable to a flock, which improve s a result by Payne and Thas. Then new and short proofs are given for a theorem of Johnson on translation generalized quadrangles and a theo rem of Glynn on ovoids.