New and updated semidefinite programming bounds for subspace codes

We show that \begin{document}$A_2(7, 4) \leq 388$\end{document} and, more generally, \begin{document}$A_q(7, 4) \leq (q^2-q+1) [7] + q^4 - 2q^3 + 3q^2 - 4q + 4$\end{document} by semidefinite programming for \begin{document}$q \leq 101$\end{document} . Furthermore, we extend results by Bachoc et al. on SDP bounds for \begin{document}$A_2(n, d)$\end{document} , where \begin{document}$d$\end{document} is odd and \begin{document}$n$\end{document} is small, to \begin{document}$A_q(n, d)$\end{document} for small \begin{document}$q$\end{document} and small \begin{document}$n$\end{document} .