Field reduction and linear sets in finite geometry

By Michel Lavrauw, Geertrui Van de Voorde. 2013

116 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/d7ec2907c6e312a58803125a995e97cffbd203d9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Yue Zhou
2. Daniele Bartoli
3. Giuseppe Marino
4. Olga Polverino
5. John Sheekey

In Discrete Mathematics and Combinatorics

1. Yue Zhou
2. Daniele Bartoli
3. Giuseppe Marino
4. Olga Polverino
5. Bence Csajbók
6. Ferdinando Zullo
7. John Sheekey

In Electrical and Electronic Engineering

1. Yue Zhou
2. Daniele Bartoli
3. Giuseppe Marino
4. Olga Polverino
5. John Sheekey

Citations in the corpus

• Maximum scattered linear sets and MRD-codes (2017, background): “For further details on linear sets see [40], [27], [28], [34], [35], [29], [12] and [13].”
• Exceptional scattered polynomials (2017, background): “For recent surveys on linear sets and particularly on the theory of scattered spaces, see [30, 31].”
• A new family of MRD-codes (2017, background): “For further details on linear sets see [34] and [23].”