RGD-systems over ${\mathbb{F}}_2$

In this paper we prove that an RGD-system over ${\mathbb{F}}_2$ with prescribed commutation relations exists if and only if the commutation relations are Weyl-invariant and can be realized in the group $U_{+}$. This result gives us a machinery to produce new examples of RGD-systems with complicated commutation relations. We also discuss some applications of this result.