A generalization of Ore's theorem on irreducible polynomials over a finite field

For an arbitrary prime power $q$, a criterion for irreducibility of a polynomial of the form
$$ F(x) = x^{q^{m}-1}+a_{m-1}x^{q^{m-1}-1}+\ldots+a_1x^{q-1}+a_0, \ a_0\neq 0, $$
over the field $K = GF(q^t)$ is established.