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Hyperovals in Desarguesian planes: An update

✍ Scribed by William Cherowitzo


Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
388 KB
Volume
155
Category
Article
ISSN
0012-365X

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In [3], W. M. Cherowitzo constructed ovals in all finite Figueroa planes of odd order. Here a class of hyperovals is constructed in the finite Figueroa planes of even order. These hyperovals are inherited from regular hyperovals in the associated desarguesian planes. It is also shown that all Figuer

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Constructions are described of maximal arcs in Desarguesian projective planes utilizing sets of conics on a common nucleus in PG(2, q). Several new infinite families of maximal arcs in PG(2, q) are presented and a complete enumeration is carried out for Desarguesian planes of order 16, 32, and 64. F

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The characterisation by Blokhuis, Ball, Brouwer, Storme, and SzΓΆnyi of certain kinds of blocking sets of RΓ©dei type is extended to specify the type of polynomial which defines the blocking set. A graphic characterisation called the profile of the set is also given, and the correspondence between the

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In this paper we show that blocking sets of cardinality less than 3(q Ο© 1)/2 (q Ο­ p n ) in Desarguesian projective planes intersect every line in 1 modulo p points. It is also shown that the cardinality of a blocking set must lie in a few relatively short intervals. This is similar to previous resul