A note on Cameron - Liebler line classes in PG(n,4)

A {\it Cameron -- Liebler line class} ${\cal L}$ with parameter $x$ is a set of lines of projective geometry $PG(3,q)$ such that each line of ${\cal L}$ meets exactly $x(q+1)+q^2-1$ lines of ${\cal L}$ and each line that is not from ${\cal L}$ meets exactly $x(q+1)$ lines of ${\cal L}$. In this paper, we obtain a classification of Cameron -- Liebler line classes in PG(3,4) and a classification of their generalization in PG(n,4), $n\geqslant 4$.