engleski

DRGs and new block designs obtained from the Mathieu groups

We describe a construction of distance-regular graphs admitting a vertex transitive action of the fi ve Mathieu groups. From the binary code spanned by an adjacency matrix of the strongly regular graph with parameters (176, 70, 18, 34) we obtain block designs having the full automorphism groups isomorphic to the Higman-Sims finite simple group. From the same code we also obtain eight 2-designs whose full automorphism group is isomorphic to the Mathieu group M22, and whose existence cannot be explained neither by the Assmus-Mattson theorem nor by a transitivity argument.

distance-regular graph ; Mathieu group ; linear code ; block design

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