**Theorem 7.1**: *A flock is a star flock if and only if the coordinate functions are linearly dependent over GF(q)*.

*Pf*: Let F = F(f,g,h) be a star flock. If P is a point in common with all the planes of F, then P must lie in W = 0, and so, P has coordinates (a,b,c,0) with not all of a, b and c being 0. Since this point lies in every plane of F, we have that:

Conversely, if the coordinate functions are linearly dependent over GF(q), then there exist elements A, B, and C in GF(q), not all 0, such that: