Designs from Maximal Subgroups and Conjugacy Classes of Finite Simple Groups

Let $G$ be a finite simple group, \(M\) be a maximal subgroup of \(G\) and \(C_g = nX\) be the conjugacy class of $G$ containing \(g\). In this paper we discuss a new method for constructing \(1-(v,k,\lambda)\) designs \(\mathcal{D} = (\mathcal{P},\mathcal{B})\), where \(\mathcal{P} = nX\) and \(\mathcal{B} = \{(M\cap nX)^y \mid y \in G\}\). The parameters \(v\), \(k\), \(\lambda\) and further properties of \(\mathcal{D}\) are determined. We also study codes associated with these designs.