Orbit codes from forms on vector spaces over a finite field

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula>-dimensional vector space over the finite field <inline-formula><tex-math id="M2">\begin{document}$ {\mathbb F_{q}} $\end{document}</tex-math></inline-formula>. All these codes admit the general linear group <inline-formula><tex-math id="M3">\begin{document}$ {{{{\rm{GL}}}}}(n,q) $\end{document}</tex-math></inline-formula> as a transitive automorphism group.</p>