Daisy structure in Desarguesian projective planes
نویسندگان
چکیده
منابع مشابه
Ovals in Desarguesian planes
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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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...
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A classical theory of Desarguesian geometry, originating with D. Hilbert in his 1899 treatise Grundlagen der Geometrie, leads from axioms to the construction of a division ring from which coordinates may be assigned to points, and equations to lines; this theory is highly nonconstructive. The present paper develops this coordinatization theory constructively, in accordance with the principles i...
متن کاملSmall weight codewords in the codes arising from Desarguesian projective planes
We study codewords of small weight in the codes arising from Desarguesian projective planes. We first of all improve the results of K. Chouinard on codewords of small weight in the codes arising from PG(2, p), p prime. Chouinard characterized all the codewords up to weight 2p in these codes. Using a particular basis for this code, described by Moorhouse, we characterize all the codewords of wei...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2003
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700003207