Nonexistence of some ternary linear codes with minimum weight -2 modulo 9

One of the fundamental problems in coding theory is to find \begin{document}$ n_q(k,d) $\end{document}, the minimum length \begin{document}$ n $\end{document} for which a linear code of length \begin{document}$ n $\end{document}, dimension \begin{document}$ k $\end{document}, and the minimum weight \begin{document}$ d $\end{document} over the field of order \begin{document}$ q $\end{document} exists. The problem of determining the values of \begin{document}$ n_q(k,d) $\end{document} is known as the optimal linear codes problem. Using the geometric methods through projective geometry and a new extension theorem given by Kanda (2020), we determine \begin{document}$ n_3(6,d) $\end{document} for some values of \begin{document}$ d $\end{document} by proving the nonexistence of linear codes with certain parameters.