Galois points for a plane curve in characteristic two

Let C be an irreducible plane curve. A point P in the projective plane is said to be Galois with respect to C if the function field extension induced by the projection from P is Galois. We denote by δ ′ ( C ) the number of Galois points contained in P 2 ∖ C . In this article we will present two results with respect to determination of δ ′ ( C ) in characteristic two. First we determine δ ′ ( C ) for smooth plane curves of degree a power of two. In particular, we give a new characterization of the Klein quartic in terms of δ ′ ( C ) . Second we determine δ ′ ( C ) for a generalization of the Klein quartic, which is related to an example of Artin–Schreier curves whose automorphism group exceeds the Hurwitz bound. This curve has many Galois points.