A sporadic ovoid in Ω+(8, 5) and some non-desarguesian translation planes of order 25
نویسندگان
چکیده
منابع مشابه
A sporadic ovoid in Omega+(8, 5) and some non-desarguesian translation planes of order 25
An ovoid is an orthogonal vector space V of type .Q + (2n, q) is a set 0 of q-1 + 1 pairwise non-orthogonal singular points (one-spaces). Every maximal singular subspace of V will contain a unique point of 0, so it is extremal. Ovoids have connections to coding theory, and translation planes (cf. Kantor [2]). There are no known examples for n 2 5 and there is evidence that they will not exist (...
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This paper surveys the known ovals in Desarguesian of even order, making use of the connection between ovals and hyperovals. First the known hyperovals are and the inequivalent m of small order arc found. The ovals contained in each of the known are determined and presented in a uniform way. Computer for new hyperovals reported. 1. OVALS AND HYPEROVALS Let PG(2, q) be the 'DC," "<"""'0" -:)"t, ...
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From this definition it readily follows that a Laguerre plane of order n has n + 1 generators, that every circle contains exactly n + 1 points and that there are n3 circles. All known models of finite Laguerre planes are of the following form. Let O be an oval in the Desarguesian projective plane P2 = PG(2, pm), p a prime. Embed P2 into threedimensional projective space P3 = PG(3, pm) and let v...
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We show that a suitable 2-dimensional linear system of Hermitian curves of PG(2, q2) defines a model for the Desarguesian plane PG(2, q). Using this model we give the following group-theoretic characterization of the classical unitals. A unital in PG(2, q2) is classical if and only if it is fixed by a linear collineation group of order 6(q + 1)2 that fixes no point or line in PG(2, q2).
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1990
ISSN: 0097-3165
DOI: 10.1016/0097-3165(90)90013-m