Definitions: Flock, Linear FlockStar Flock, Thick Cone, Herd Space, Herd

Corollary 11.1.1: If q is a prime, then all star flocks of thick cones are linear.

Pf: The cases of q = 2 (Proposition 4.1 [back]) and q = 3 (Proposition 9.1 [back]) have already been dealt with. So, we may assume that q is a prime > 3. Since a prime field has no proper subfields, there are no pe-linearized polynomials other than the linear ones, so by Theorem 11.1.3 [back] there are no proper star flocks.

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