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In this work, we define three composite matrices derived from group rings. We employ these composite matrices to create generator matrices of the form   \begin{document}$ [I_n \ | \ \Omega(v)], $\end{document}   where   \begin{document}$ I_n $\end{document}   is the identity matrix and   \begin{document}$ \Omega(v) $\end{document}   is a composite matrix and search for binary self-dual codes with parameters   \begin{document}$ [36,18, 6 \ \text{or} \ 8]. $\end{document}   We next lift these codes over the ring   \begin{document}$ R_1 = \mathbb{F}_2+u\mathbb{F}_2 $\end{document}   to obtain codes whose binary images are self-dual codes with parameters   \begin{document}$ [72,36,12]. $\end{document}   Many of these codes turn out to have weight enumerators with parameters that were not known in the literature before. In particular, we find   \begin{document}$ 30 $\end{document}   new Type I binary self-dual codes with parameters   \begin{document}$ [72,36,12]. $\end{document}

New type i binary [72, 36, 12] self-dual codes from composite matrices and <i>R</i><sub>1</sub> lifts