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Difference Sets In Abelian 2-Groups, James A. Davis

Department of Math & Statistics Faculty Publications

Examples of difference sets are given for large classes of abelian groups of order 2^{2d + 2}. This fills in the gap of knowledge between Turyn's exponent condition and Dillon's rank condition. Specifically, it is shown thatℤ/(2^d)×ℤ/(2^d+2) andℤ/(2^d+1)×Z/(2^d+1) both admit difference sets, and these have many implications.