Isotropic subspace of a binary symplectic space ($\omega {|}_{L\times L}=0$)

A subspace $L$ is isotropic when the symplectic pairing vanishes between every pair of its vectors. Its binary Pauli labels therefore commute. Nondegeneracy identifies the ambient space with its dual, so the map to $L^{\ast }$ is surjective and $\dim L^{\perp }=2n-\dim L$. Since $L\subseteq L^{\perp }$, it follows that $\dim L\le n$. This explains the maximum number of independent generators of a stabilizer group.