In this paper we show that blocking sets of cardinality less than 3(q ϩ 1)/2 (q ϭ p n ) in Desarguesian projective planes intersect every line in 1 modulo p points. It is also shown that the cardinality of a blocking set must lie in a few relatively short intervals. This is similar to previous resul
Rédei Blocking Sets in Finite Desarguesian Planes
✍ Scribed by B.F. Sherman
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 272 KB
- Volume
- 98
- Category
- Article
- ISSN
- 0097-3165
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✦ Synopsis
The characterisation by Blokhuis, Ball, Brouwer, Storme, and Szönyi of certain kinds of blocking sets of Rédei type is extended to specify the type of polynomial which defines the blocking set. A graphic characterisation called the profile of the set is also given, and the correspondence between the two is demonstrated with relatively small polynomial sizes.
📜 SIMILAR VOLUMES
A generalisation is given to recent results concerning the possible number of nuclei to a set of points in PG(n, q). As an application of this we obtain new lower bounds on the size of a t-fold blocking set of AG(n, q) in the case (t, q)>1.
## Abstract In this paper, we show that there are at least __cq__ disjoint blocking sets in PG(2,__q__), where __c__ ≈ 1/3. The result also extends to some non‐Desarguesian planes of order __q__. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 149–158, 2006
We study minimal blocking sets in PG(2, q) having q+m points outside some fixed line. If 0<m<(-q)Â2 then either the blocking set is large, or every line contains 1 mod p points of the blocking set, where p is the characteristic of the field GF(q). 1997 Academic Press 1. INTRODUCTION A blocking set i
We prove that the number of directions determined by a set of p points in AG(2, p), p prime, cannot be between ( p+3)Â2 and ( p&1)Â2+ 1 3 -p. This is equivalent to saying that besides the projective triangle, every blocking set of Re dei type in PG(2, p) has size at least 3( p&1)Â2+ 1 3 -p.