Classes and equivalence of linear sets in $PG(1,q^n)$

TL;DR

This paper investigates the classification and equivalence of linear sets in projective lines over finite fields, exploring their connections to varieties, blocking sets, and MRD-codes.

Contribution

It provides a comprehensive analysis of the equivalence problem for linear sets in PG(1,q^n), linking geometric and coding-theoretic structures.

Findings

Characterization of linear set equivalence classes

Connections between linear sets and MRD-codes

Insights into associated varieties and blocking sets

Abstract

The equivalence problem of $\mathbb{F}_q$-linear sets of rank n of $PG(1,q^n)$ is investigated, also in terms of the associated variety, projecting configurations, $\mathbb{F}_q$-linear blocking sets of R\'edei type and MRD-codes.