Study on algebraic or combinatorial structures whose automorphism groups contain finite simple groups

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We have studied some algebraic structures and combinatorial structured whose automorphism groups contain finite simple groups.(1) We have studied the binary code spanned by the sets of fixed points of the involutions of a finite transitive permutation group and its dual code. New self-dual codes invariant under the Hall-Janko group and the Rudvalis group have been constructed, respectively.(2) We have studied rank 3 graphs related to some sporadic simple groups (especially, HJ, Suz, M24). New constructions of these rank 3 graphs from some designs have been obtained.(3) We have determined the minimum value m such that a given Niemeier lattice is a m-neighbor of the Leech lattice.