Field reduction and linear sets in finite geometry

2013/10/31 by Lavrauw, Michel, Van de Voorde, Geertrui · 5 citations
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1310.8522

Abstract

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 paper we elaborate on this technique. Field reduction for projective and polar spaces is formalized and the links with Desarguesian spreads and linear sets are explained in detail. Recent results and some fundamental ques- tions about linear sets and scattered spaces are studied. The relevance of field reduction is illustrated by discussing applications to blocking sets and semifields.

Cited by

• On the weight distribution of linear sets with complementary weights and related constructions
• Regular fat linear sets
• Delsarte duality on subspaces and applications to rank-metric codes and q-matroids
• Clubs in projective spaces and three-weight rank-metric codes
• Towards the classification of maximum scattered linear sets of PG(1,q⁵)

Related

• Desarguesian spreads and field reduction for elements of the semilinear group
• How to use finite fields for problems concerning infinite fields
• On cutting blocking sets and their codes
• On Geometry and Combinatorics of Finite Classical Polar Spaces
• Linear sets from projection of Desarguesian spreads