Generic automorphism conjecture for hyperelliptic curves of 2-rank zero

Let $C$ be a generic hyperelliptic curve of genus $g$ and $2$-rank $0$ over a field of characteristic $2$. Generic automorphism conjecture for 2-rank-zero hyperelliptic curves. If $g>2$, then

$$\operatorname{Aut}(C)=\{\pm 1\}.$$

The paper verifies the assertion for $2<g\leq 6$ using its computed group structures, while the statement remains conjectural for larger genus.