Yet Another Distance-Regular Graph Related to a Golay Code

We describe a new distance-regular, but not distance-transitive, graph. This graph has intersection array {110, 81, 12; 1, 18, 90}, and automorphism group M22: 2. In [1], Brouwer, Cohen and Neumaier discuss many distance-regular graphs related to the famous Golay codes. In this note, we describe yet another such graph. Ivanov, Linton, Lux, Saxl and the author [4] have classified all primitive distance-transitive representations of the sporadic simple groups and their automorphism groups. As part of this work, all multiplicity-free primitive representations of such groups have also been classified. One such representation is M22: 2 on the cosets of L2(11): 2. This representation has rank 6, with subdegrees 1, 55, 55, 66, 165, 330. Let Γ be the graph obtained by the edge-union of the orbital graphs corresponding to the two suborbits of length 1991 Mathematics Subject Classification: 05E30, 05C25