Difference Sets and Hyperovals

  • Authors:
  • Antonio Maschietti

  • Affiliations:
  • Dipartimento di Matematica G. Castelnuovo, Universita‘ La Sapienza, Roma. E-mail: maschiet@mat.uniromal.it

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 1998

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Abstract

We construct three infinite families of cyclic differencesets, using monomial hyperovals in a desarguesian projectiveplane of even order. These difference sets give rise to cyclicHadamard designs, which have the same parameters as the designsof points and hyperplanes of a projective geometry over the fieldwith two elements. Moreover, they are substructures of the Hadamarddesign that one can associate with a hyperoval in a projectiveplane of even order.