On Some Transitive Combinatorial Structures and Codes Constructed From the Symplectic Group $S(6,2)$

Abstract

We describe the construction of transitive $2$-designs and strongly regular graphs defined on the conjugacy classes of the maximal and second maximal subgroups of the symplectic group $S(6,2)$. Furthermore, we present linear codes invariant under the action of the group $S(6,2)$ obtained as the codes of the constructed designs and graphs.