Cameron-Liebler line classes with parameter x=q2−12

In this paper, we give an algebraic construction of a new infinite family of Cameron-Liebler line classes with parameter x=q2−12 for q≡5 or 9(mod12), which generalizes the examples found by Rodgers in [26] 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 AG(2,q), which is closely related to our Cameron-Liebler line classes.