Distance-regular graphs obtained from the Mathieu groups $M_{11}$, $M_{12}$, $M_{22}$, $M_{23}$ and $M_{24}$

Dean Crnkovic, Nina Mostarac, Andrea Svob

Published 2021-01-07Version 1

We construct distance-regular graphs (including strongly regular graphs) admitting a transitive action of the five sporadic simple groups discovered by E. Mathieu, the Mathieu groups $M_{11}$, $M_{12}$, $M_{22}$, $M_{23}$ and $M_{24}$. We discuss a possibility of permutation decoding of the codes spanned by the adjacency matrices of these graphs and find PD-sets for some of the codes.