Menon difference sets have parameters (4N2, 2N2 − N, N2 − N). These have been constructed for N = 2a3b, 0 ⩽ a,b, but the only known constructions in abelian groups require that the Sylow 3-subgroup be elementary abelian (there are some nonabelian examples). This paper provides a construction of difference sets in higher exponent groups, and this provides new examples of perfect binary arrays.
Copyright © 1993, Elsevier. This article first appeared in Journal of Combinatorial Theory, Series A: 64:2 (1993), 329-336.
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Arasu, K. T., James A. Davis, Jonathan Jedwab, and Surinder K. Sehgal. "New Constructions of Menon Difference Sets." Journal of Combinatorial Theory, Series A 64, no. 2 (November 1993): 329-36. doi: 10.1016/0097-3165(93)90101-D.