A recurrent method for constructing irreducible polynomials over finite fields

Authors:
Sergey Abrahamyan;Melsik Kyureghyan
Affiliations:
Institute of Informatics and Automation Problems, Yerevan, Armenia;Institute of Informatics and Automation Problems, Yerevan, Armenia
Venue:
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Year:
2011

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Abstract

In this paper we consider irreducibility of the polynomial composition of the form (xp - x + δ2)n P (xp-x+δ1/xp-x+δ2) ver Fq under certain conditions. Furthermore, a computationally simple and explicit method of constructing recursive sequences of irreducible polynomials of degree npk (k = 1, 2, 3, ... ) over Fq is given.