Orbit codes from forms on vector spaces over a finite field

In this paper we construct different families of orbit codes in the vector spaces of the symmetric bilinear forms, quadratic forms and Hermitian forms on an \begin{document}$ n $\end{document}-dimensional vector space over the finite field \begin{document}$ {\mathbb F_{q}} $\end{document}. All these codes admit the general linear group \begin{document}$ {{{{\rm{GL}}}}}(n,q) $\end{document} as a transitive automorphism group.