We provide a new construction of the strongly regular graphs associated with the two sporadic simple groups M22 and HS. Further, we give some new constructions of other known strongly regular graphs by taking the orbits of a certain subgroup of M22 on the planes of the Hermitian variety H(5, 4). These geometric constructions can be used to produce cap codes with large parameters and automorphism groups containing M22 as a subgroup.
['Antonio Cossidente', 'Angelo Sonnino']
On graphs and codes associated to the sporadic simple groups HS and M 22