منابع مشابه
Groups of Maximal Arcs
Apart from hyperovals and their duals there are only three classes of maximal arcs known in Desarguesian projective planes. Two classes are due to J. A. Thas and one to R. H. F. Denniston. In this paper collineation stabiliser and isomorphism problems for those maximal arcs in Desarguesian projective planes are examined. The full collineation stabilisers of the known maximal arcs are calculated...
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A lower bound on the minimum degree of the plane algebraic curves containing every point in a large point-set K of the Desarguesian plane PG(2, q) is obtained. The case where K is a maximal (k, n)-arc is considered in greater depth.
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A ( k , n ) a r c in a projective plane is a set of k points, at most n on every line. If the order of the plane is q, then k < 1 + (q + 1) (n 1) = qn q + n with equality if and only if every line intersects the arc in 0 or n points. Arcs realizing the upper bound are called maximal arcs. Equality in the bound implies tha t n lq or n = q + l . If 1 < n < q, then the maximal arc is called non-tr...
متن کاملA geometric approach to Mathon maximal arcs
In 1969, Denniston gave a construction of maximal arcs of degree d in Desarguesian projective planes of even order q, for all d dividing q. In 2002 Mathon gave a construction method generalizing the one of Denniston. We will give a new geometric approach to these maximal arcs. This will allow us to count the number of non-isomorphic Mathon maximal arcs of degree 8 in PG(2, 2h), h 6= 7 and prime...
متن کاملMaximal arcs and quasi-symmetric designs
In 2001, Blokhuis and Haemers gave an interesting construction for quasisymmetric designs with parameters 2-(q, q(q − 1)/2, q(q − q − 2)/4) and block intersection numbers q(q − 2)/4 and q(q − 1)/4 (where q ≥ 4 is a power of 2), which uses maximal arcs in the affine plane AG(2, q) and produces examples embedded into affine 3-space AG(3, q). We consider this construction in more detail and in a m...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2001
ISSN: 0097-3165
DOI: 10.1006/jcta.2000.3126