Some new examples of flocks of \(Q^+(3,q)\) (Q1112324)

After some preliminary results, the author exhibits some new examples of flocks of \(Q^+(3,q)\), that is of partition of the non-singular ruled quadric \(Q^+(3,q)\) of PG(3,q) into disjoint irreducible conics. Theorem 2: for \(q=11,23,59\) there exist a flock which is neither linear nor a Thas flock. A flock is called linear if its conics belong to planes through a line (the axis of the flock); and it is a Thas flock if the conics belong to planes through a line \(\ell_ 1\) or its polar \(\ell_ 2\) (with respect to \(Q^+(3,q))\).