Designs from Maximal Subgroups and Conjugacy Classes of Finite Simple Groups

Abstract

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.