We construct three infinite families of cyclic difference sets, using monomial hyperovals in a desarguesian projective plane of even order. These difference sets give rise to cyclic Hadamard designs, which have the same parameters as the designs of points and hyperplanes of a projective geometry over the field with two elements. Moreover, they are substructures of the Hadamard design that one can associate with a hyperoval in a projective plane of even order.
Difference sets and hyperovals / Maschietti, Antonio. - In: DESIGNS, CODES AND CRYPTOGRAPHY. - ISSN 0925-1022. - STAMPA. - 14:(1998), pp. 89-98.
Difference sets and hyperovals
MASCHIETTI, Antonio
1998
Abstract
We construct three infinite families of cyclic difference sets, using monomial hyperovals in a desarguesian projective plane of even order. These difference sets give rise to cyclic Hadamard designs, which have the same parameters as the designs of points and hyperplanes of a projective geometry over the field with two elements. Moreover, they are substructures of the Hadamard design that one can associate with a hyperoval in a projective plane of even order.File allegati a questo prodotto
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