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

研究了自同构群包含有限单群的代数结构和组合结构。(1)研究了有限传递置换群的对偶码及其对偶对偶对合对合对合的不动点集所张成的二进制码。分别构造了Hall-Janko群和Rudvalis群下的新的自对偶码不变量。(2)我们研究了一些零星的简单群（特别是HJ， Suz, M24）的秩3图。从一些设计中得到了这些3阶图的新构造。(3)我们确定了最小值m，使得给定的Niemeier格是Leech格的m近邻。

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.