On automorphisms of a distance-regular graph with intersection array $\{243,220,1;1,22,243\}$

It was proved that a distance-regular graph in which neighborhoods of vertices are strongly regular with parameters $(245,64,18,16)$ has intersection array $\{243,220,1;1,22,243\}$ or $\{243,220,1;1,4,243\}$. In this paper we found the automorphisms of a distance regular graph with intersection array $\{243,220,1;1,22,243\}$. It is proved that a vertex-transitive distance-regular graph with intersection array $\{243,220,1;1,22,243\}$ is the arc-transitive Mathon graph affording the group $L_2(3^5)$.