Multiplicative Difference Sets via Additive Characters

  • Authors:
  • J. F. Dillon

  • Affiliations:
  • National Security Agency, Fort George G. Meade, MD 20755

  • Venue:
  • Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
  • Year:
  • 1999

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Abstract

Weuse Fourier analysis on the additive group of \GFto give an alternative proof of the recent theorem of Maschiettiand to prove recent conjectures of No, Chung and Yun and No,Golomb, Gong, Lee and Gaal on difference sets in the multiplicativegroup of \GF, m odd. Along the aye prove a stronger form of a celebrated theorem of Welch onthe 3-valued cross-correlation of maximal lengthsequences.