$\Gamma$-conjugate weight enumerators and invariant theory

Gabriele Nebe, Leonie Scheeren

Let $K$ be a field, $\Gamma$ a finite group of field automorphisms of $K$, $F$ the $\Gamma$-fixed field in $K$ and $G\le$GL${}_v(K)$ a finite matrix group. Then the action of $\Gamma$ defines a g…