Abstract
We use Fourier analysis on the additive group of \(\mathbb{F}_{2^m }\) to give an alternative proof of the recent theorem of Maschietti and to prove recent conjectures of No, Chung and Yun and No, Golomb, Gong, Lee and Gaal on difference sets in the multiplicative group of \(\mathbb{F}_{2^m }\), m odd. Along the ay e prove a stronger form of a celebrated theorem of Welch on the 3-valued cross-correlation of maximal length sequences.
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Dillon, J.F. Multiplicative Difference Sets via Additive Characters. Designs, Codes and Cryptography 17, 225–235 (1999). https://doi.org/10.1023/A:1026435428030
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DOI: https://doi.org/10.1023/A:1026435428030