Examples of difference sets are given for large classes of abelian groups of order 22d + 2. This fills in the gap of knowledge between Turyn's exponent condition and Dillon's rank condition. Specifically, it is shown thatℤ/(2d)×ℤ/(2d+2) andℤ/(2d+1)×Z/(2d+1) both admit difference sets, and these have many implications.
Copyright © 1991, Elsevier. This article first appeared in Journal of Combinatorial Theory, Series A: 57:2 (1991), 262-286.
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Davis, James A. "Difference Sets in Abelian 2-Groups." Journal of Combinatorial Theory, Series A 57, no. 2 (July 1991): 262-86. doi: 10.1016/0097-3165(91)90050-Q.