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Jacobi-like sums and difference sets with Singer parameters

We show that a function F : F2m → C whose multiplicative Fourier coefficients are given by certain character sums, which we call Jacobi-like sums, is in fact the ±1-valued characteristic function of a difference set in F2m with Singer parameters. We show further that the difference sets arising from such functions are precisely the so-called DD difference sets constructed by the first author and Hans Dobbertin.