Applications of the DFT to Abelian difference sets (Q1093642)

We use methods derived from the discrete Fourier transform (DFT) to study Abelian difference sets. We give an easy proof of Hall's multiplier theorem and new proofs of results due to \textit{H. A. Wilbrink} [J. Comb. Theory, Ser. A 38, 94-95 (1985; Zbl 0554.05012)] and \textit{D. Ghinelli- Smit} [Arch. Math. 44, 282-288 (1985; Zbl 0571.51005)]. We show a partial converse of Wilbrink's theorem. We also give a method to restrict the possible values of the dimension of GF(p)-codes resulting from Abelian difference sets.