منابع مشابه
Hyperovals
We investigate elations and generalised homologies stabilising hyperovals in arbitrary projective planes of even order. In particular, examples of such stabilisers are given which include the known hyperovals in PG(2, q) and the recently constructed hyperovals in the projective planes of order 16 [18]. We also give a proof that the infinite family of hyperovals constructed by Cherowitzo [3, 2] ...
متن کاملGeometric Codes and Hyperovals
Geometric Codes and Hyperovals Anton Betten Department of Mathematics Colorado State University Fort Collins, Co 80523 U.S.A [email protected] I will outline the theory of Geometric Codes and their relationship to the construction of hyperovals in Desarguesian projective planes of even order.
متن کاملOn the Classification of Hyperovals
A hyperoval in the projective plane P(Fq) is a set of q + 2 points no three of which are collinear. Hyperovals have been studied extensively since the 1950s with the ultimate goal of establishing a complete classification. It is well known that hyperovals in P(Fq) are in one-to-one correspondence to polynomials with certain properties, called o-polynomials of Fq. We classify o-polynomials of Fq...
متن کاملHyperovals in Desarguesian planes: An update
Recent progress in the study of hyperovals in Desarguesian planes of even order has been rapid and the need for an updated survey is clear. We will present the most recent findings and provide some open problems and directions for future research.
متن کاملOn hyperovals of polar Grassmannians
A hyperoval of a point-line geometry is a nonempty set of points meeting each line in either 0 or 2 points. In this paper, we study hyperovals in line Grassmannians of finite polar spaces of rank 3, hereby often imposing some extra regularity conditions. We determine an upper bound and two lower bounds for the size of such a hyperoval. If equality occurs in one of these bounds, then there is an...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1991
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(13)80007-8