The isomorphism of the Cohen, Haemers-van Lint and de Clerk-Dye-Thas partial geometries
A. M. Cohen constructed a partial geometry pg(8,9,4) using group theory. Independently, using coding theory, W. Haemers and J. H. van Lint obtained a partial geomery with the same parameters. Later on, F. De Clerk, R.H. Dye and the reviewer described an infinite class of partial geometries \(pg(2^{2n-1},2^{2n-1}+1,2^{2n-2})\). So for \(n=2\) there arises again a pg(8,9,4). In ''Strongly regular graphs defined by spreads ''[Israel J. Math. 41, 298-312 (1982; Zbl 0524.05020)], \textit{W. M. Kantor} proved that the pg(8,9,4)'s of Haemers-van Lint and De Clerck-Dye-Thas are isomorphic. Here Tonchev proves the isomorphism between the pg(8,9,4)'s of Cohen and Haemers-van Lint.
scientific article; zbMATH DE number 3859874