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.
On Intersection Sets in Desarguesian Affine Spaces
β Scribed by Simeon Ball
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 87 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
β¦ Synopsis
Lower bounds on the size of t-fold blocking sets with respect to hyperplanes or t-intersection sets in AG(n, q) are obtained, some of which are sharp.
π SIMILAR VOLUMES
In this paper we show that blocking sets of cardinality less than 3(q Ο© 1)/2 (q Ο 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
In [Blokhuis and Lavrauw (Geom. Dedicata 81 (2000), 231-243)] a construction of a class of two-intersection sets with respect to hyperplanes in PGΓ°r Γ 1; q t Γ; rt even, is given, with the same parameters as the union of Γ°q t=2 Γ 1Γ=Γ°q Γ 1Γ disjoint Baer subgeometries if t is even and the union of Γ°
Intersection sets and blocking sets play an important role in contemporary finite geometry. There are cryptographic applications depending on their construction and combinatorial properties. This paper contributes to this topic by answering the question: how many circles of an inversive plane will b
## Abstract In this paper the concepts of strictly convex and uniformly convex normed linear spaces are extended to metric linear spaces. A relationship between strict convexity and uniform convexity is established. Some existence and uniqueness theorems on best approximation in metric linear space