suppose that $k$ is a finite field of characteristic 2 and $(V,q)$ a quadratic space, i.e., $V$ is a $k$-vector space and $q:V\to k$ quadratic form. Suppose that $\dim(V)\geq 4$ and that $q$ is non-defective, i.e., the $k$-bilinear $B(x,y)=q(x+y)-q(x)-q(y)$ is non-degenerated:
The question is:
Given a non-singular vector $0\neq v\in V$, (that is $q(v)\neq 0$), What is the isomorphism type of the stabilizer of $v$ in $O'(V,q)$?
Note: I know the answer in the case that $k=\mathbb F_2$. In this case the stabilizer is $O(2n-1,2)\cong Sp(2n-2,2)$, where $2n=\dim(V)$ (but I do not have a reference). I suppose that the same is true in general, that is the stabilizer of a non-singular vector is isomorphic to $Sp(2n-2,k)$.