Derivation of Cameron-Liebler line classes

TL;DR

This paper introduces an infinite family of Cameron-Liebler line classes in projective 3-space with a specific parameter, expanding the known examples in finite geometry.

Contribution

It constructs a new infinite family of Cameron-Liebler line classes with a particular parameter for all odd q, advancing the understanding of these geometric objects.

Findings

Constructed an infinite family of line classes for all odd q

Established the parameter x = (q^2 + 1)/2 for these classes

Contributed to the classification of Cameron-Liebler line classes

Abstract

We construct a new infinite family of Cameron-Liebler line classes in $PG(3,q)$ with parameter $x=\frac{q^2+1}{2}$ for all odd $q$.