# A small minimal blocking set in PG(n, pt), spanning a (t − 1)-space, is linear

@article{Sziklai2013ASM,
title={A small minimal blocking set in PG(n, pt), spanning a (t − 1)-space, is linear},
author={P{\'e}ter Sziklai and Geertrui Van de Voorde},
journal={Designs, Codes and Cryptography},
year={2013},
volume={68},
pages={25-32}
}
• Published 3 October 2012
• Mathematics
• Designs, Codes and Cryptography
In this paper, we show that a small minimal blocking set with exponent e in PG(n, pt), p prime, spanning a (t/e − 1)-dimensional space, is an $${\mathbb{F}_{p^e}}$$ -linear set, provided that p > 5(t/e)−11. As a corollary, we get that all small minimal blocking sets in PG(n, pt), p prime, p > 5t − 11, spanning a (t − 1)-dimensional space, are $${\mathbb{F}_p}$$ -linear, hence confirming the linearity conjecture for blocking sets in this particular case.
4 Citations
Field reduction in nite projective geometry
In this talk, we will discuss the relevance of field reduction in the area of finite projective geometry; we will present some classical constructions that can be obtained via this technique as well
Applications of Polynomials Over Finite Fields
A most efficient way of investigating combinatorially defined point sets in spaces over finite fields is associating polynomials to them. This technique was first used by Rédei, Jamison, Lovász,
Field reduction and linear sets in finite geometry
• Mathematics
• 2013
Based on the simple and well understood concept of subfields in a finite field, the technique called `field reduction' has proved to be a very useful and powerful tool in finite geometry. In this
Finite Geometry and Combinatorial Applications
1. Fields 2. Vector spaces 3. Forms 4. Geometries 5. Combinatorial applications 6. The forbidden subgraph problem 7. MDS codes Appendix A. Solutions to the exercises Appendix B. Additional proofs