Galois points for a plane curve in characteristic two

Let C$C$ be an irreducible plane curve. A point P$P$ in the projective plane is said to be Galois with respect to C$C$ if the function field extension induced by the projection from P$P$ is Galois. We denote by δ^′(C)${\delta }^{\prime }\left(C\right)$ the number of Galois points contained in P²?C${\mathbb{P}}^2?C$. In this article we will present two results with respect to determination of δ^′(C)${\delta }^{\prime }\left(C\right)$ in characteristic two. First we determine δ^′(C)${\delta }^{\prime }\left(C\right)$ 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)${\delta }^{\prime }\left(C\right)$. Second we determine δ^′(C)${\delta }^{\prime }\left(C\right)$ 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.