Nonexistence of certain perfect arrays
The authors show that if an abelian group \(G=H \times Z_ a \times Z_ b\), where \(| H |\) is even and \(ab\) is an even power of an odd prime \(p\) that is self-conjugate modulo exp \(H\) and does not divide \(| H |\), contains a Menon difference set, then \(a=b\) and \(p<| H |\). This result, together with the equivalence between perfect binary arrays and Menon difference sets in certain groups, is then exploited to establish the nonexistence of certain perfect binary arrays.
scientific article; zbMATH DE number 562653
scientific article