# A class of linear sets in PG(1,q^5)

## TL;DR

This paper explores a broad class of linear sets in PG(1,q^5), identifying conditions for the existence of new maximum scattered linear sets, extending previous classifications for n ≤ 4.

## Contribution

It introduces a wide parametric class of linear sets in PG(1,q^5) and establishes conditions for their maximal scatteredness, advancing the understanding beyond prior classifications.

## Key findings

- Conditions for new maximum scattered linear sets in PG(1,q^5)
- Extension of classification from n ≤ 4 to n=5
- Identification of parameters influencing scatteredness

## Abstract

The maximum scattered linear sets in $PG(1,q^n)$ have been completely classified for $n \le 4$ by Csajb\'ok-Zanella and Lavrauw-Van de Voorde. Here a wide class of linear sets in $PG(1,q^5)$ is studied which depends on two parameters. Conditions for the existence, in this class, of possible new maximum scattered linear sets in $PG(1,q^5)$ are exhibited.