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finite field; irreducible polynomial; iterative construction

References:

[1] Cohen, S. D.: **The explicit construction of irreducible polynomials over finite fields**. Des. Codes Cryptography 2 (1992), 169-174. DOI 10.1007/BF00124895 | MR 1171532

[2] Green, D. H., Taylor, I. S.: **Irreducible polynomials over composite Galois fields and their applications in coding techniques**. Proc. Inst. Elec. Engrs. 121 (1974), 935-939. MR 0434611

[3] Kyuregyan, M. K.: **Iterated constructions of irreducible polynomials over finite fields with linearly independent roots**. Finite Fields Appl. 10 (2004), 323-341. MR 2067602

[4] Kyuregyan, M. K.: **Recurrent methods for constructing irreducible polynomials over {$ GF(2)$}**. Finite Fields Appl. 8 (2002), 52-68. MR 1872791

[5] Meyn, H.: **On the construction of irreducible self-reciprocal polynomials over finite fields**. Appl. Algebra Eng. Commun. Comput. 1 (1990), 43-53. DOI 10.1007/BF01810846 | MR 1325510

[6] Mullen, G. L., Panario, D.: **Handbook of Finite Fields**. Discrete Mathematics and Its Applications CRC Press, Boca Raton (2013). MR 3087321

[7] Ugolini, S.: **Sequences of irreducible polynomials without prescribed coefficients over odd prime fields**. Des. Codes Cryptography 75 (2015), 145-155. DOI 10.1007/s10623-013-9897-1 | MR 3320357

[8] Ugolini, S.: **Sequences of binary irreducible polynomials**. Discrete Math. 313 (2013), 2656-2662. DOI 10.1016/j.disc.2013.08.011 | MR 3095441

[9] Ugolini, S.: **Graphs associated with the map {$x\mapsto x+x^{-1}$} in finite fields of characteristic two**. Theory and Applications of Finite Fields. Conf. on finite fields and their applications, Ghent, Belgium, 2011 American Mathematical Society, Contemporary Mathematics 579 Providence (2012), 187-204 M. Lavrauw et al. MR 2975769

[10] Varšamov, R. R., Garakov, G. A.: **On the theory of selfdual polynomials over a Galois field**. Bull. Math. Soc. Sci. Math. Répub. Soc. Roum., Nouv. Sér. 13 Russian (1969), 403-415. MR 0297454