$M$-matrices of the Ternary Golay Code and the Mathieu Group $M_{12}$
Maro Kimizuka, Ryuji Sasaki · Tokyo Journal of Mathematics · 2008
In this article, we define $M$-matrices of the ternary Golay code and build fundamental properties of the ternary Golay code on $M$-matrices. Moreover, using four $M$-matrices of the ternary Golay code, we give order three elements, in the Mathieu group $M_{12}$, which generate $M_{11}$ and $M_{12}$.