Impossibility of a Certain Cyclotomic Equation with Applicationsto Difference Sets

  • Authors:

  • K. T. Arasu;Alexander Pott

  • Affiliations:

  • Department of Mathematics and Statistics, Wright State University, Dayton, Ohio 45435, USA;Institut für Mathematik der Universität Augsburg, 86135 Augsburg, Germany

  • Venue:
  • Designs, Codes and Cryptography - Special issue dedicated to Hanfried Lenz
  • Year:
  • 1996

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Abstract

Under certain conditions, we show the nonexistence ofan element \gamma in the p-th cyclotomicfield over \bQ, that satisfies \gamma \bar{\gamma}= n. As applications, we establish the nonexistence ofsome difference sets and affine difference sets.