On primitive elements of finite fields avoiding affine hyperplanes

Let n≥2 be an integer and let Fq be the finite field with q elements, where q is a prime power. Given Fq-affine hyperplanes A1,…,An of Fqn in general position, we study the existence and distribution of primitive elements of Fqn, avoiding each Ai. We obtain both asymptotic and concrete results, rela...

Full description

Saved in:
Bibliographic Details
Published in:Finite fields and their applications 2021-12, Vol.76, p.101911, Article 101911
Main Authors: Fernandes, Arthur, Reis, Lucas
Format: Article
Language:English
Subjects:
Affine spaces
Character sums
Finite fields
Primitive elements
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let n≥2 be an integer and let Fq be the finite field with q elements, where q is a prime power. Given Fq-affine hyperplanes A1,…,An of Fqn in general position, we study the existence and distribution of primitive elements of Fqn, avoiding each Ai. We obtain both asymptotic and concrete results, relating to past works on digits over finite fields.
ISSN:1071-5797
1090-2465
DOI:10.1016/j.ffa.2021.101911