On plane curves given by separated polynomials and their automorphisms (Q2301365)

Let \(C\) be a plane curve defined over the algebraic closure of the field \(\mathbb {F}_p\) and defined in the affine plane by \(A(y) =x^m\) with \(A(y)\) an additive polynomial and \((m,p)=1\). The authors compute the automorphism group of \(C\) when \(m \ncong 1\pmod{p}\). For a curve \(X\) of separable type \(A(y) =B(x)\) they gives conditions on \(\mathrm{Aut}(X)\) assoring that \(B(x) =x^m\). They also compute the automorphism groups of the norm-trace curves. All these results are used to compute the automorphism groups of certain one-point AG codes.