New lower bounds on the size of (n,r)-arcs in PG(2,q)

被引：4
|
作者：
Braun, Michael [1 ]
机构：
[1] Univ Appl Sci, Fac Comp Sci, Darmstadt, Germany
来源：
JOURNAL OF COMBINATORIAL DESIGNS | 2019年 / 27卷 / 11期
关键词：
arcs; integer linear programming; linear code; R)-ARCS; SETS;
D O I：
10.1002/jcd.21672
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
An (n,r)-arc in PG(2,q) is a set of n points such that each line contains at most r of the selected points. It is well known that (n,r)-arcs in PG(2,q) correspond to projective linear codes. Let mr(2,q) denote the maximal number n of points for which an (n,r)-arc in PG(2,q) exists. In this paper we obtain improved lower bounds on mr(2,q) by explicitly constructing (n,r)-arcs. Some of the constructed (n,r)-arcs correspond to linear codes meeting the Griesmer bound. All results are obtained by integer linear programming.
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页码：682 / 687
页数：6
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