Geodesic
A generalization of Ore's theorem on irreducible polynomials over a finite field
Diskretnaya Matematika, Tome 27 (2015) no. 1, pp. 108-110

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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.
Keywords: irreducible polynomials, irreducibility criterion. 
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     author = {A. A. Nechaev and V. O. Popov},
     title = {A generalization of {Ore's} theorem on irreducible polynomials over a finite field},
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     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2015_27_1_a7/}
}
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A. A. Nechaev; V. O. Popov. A generalization of Ore's theorem on irreducible polynomials over a finite field. Diskretnaya Matematika, Tome 27 (2015) no. 1, pp. 108-110. http://geodesic.mathdoc.fr/item/DM_2015_27_1_a7/