An Algorithm for Constructing Some Maximal Arcs in PG(2, q 2)
نویسندگان
چکیده
منابع مشابه
New Large (n, r)-arcs in PG(2, q)
An $(n, r)$-arc is a set of $n$ points of a projective plane such that some $r$, but no $r+1$ of them, are collinear. The maximum size of an $(n, r)$-arc in $PG(2, q)$ is denoted by $m_r(2,q)$. In this paper we present a new $(184,12)$-arc in PG$(2,17),$ a new $(244,14)$-arc and a new $(267,15$)-arc in $PG(2,19).$
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In this paper we show that there are several other structures that arise from the functions associated with the maximal arcs of Mathon type. So it is shown that maximal arcs of Mathon type are equivalent to additive partial flocks of the quadratic cone in PG(3, q) and to additive partial q-clans. Further they yield partial ovoids of Q(5, q), partial spreads of lines of PG(3, q), translation k-a...
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A (k; n)-arc in PG(2; q) is usually deened to be a set K of k points in the plane such that some line meets K in n points but such that no line meets K in more than n points. There is an extensive literature on the topic of (k; n)-arcs. Here we keep the same deenition but allow K to be a multiset, that is, permit K to contain multiple points. The case k = q 2 + q + 2 is of interest because it i...
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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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ژورنال
عنوان ژورنال: Results in Mathematics
سال: 2008
ISSN: 1422-6383,1420-9012
DOI: 10.1007/s00025-007-0268-y