In this paper, we give an algebraic construction of a new infinite family of Cameron-Liebler line classes with parameter $x=\frac{ q^2-1}{ 2}$ for $q\equiv 5$ or $9\pmod{ 12}$, which generalizes the examples found by Rodgers in \cite{ rodgers} through a computer search. Furthermore, in the case where $q$ is an even power of $3$, we construct the first infinite family of affine two-intersection sets in $\mathrm{ AG}(2,q)$.
Categories: math.CO