Geodesic
On an iterated construction of irreducible polynomials over finite fields of even characteristic by Kyuregyan
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 243-250 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We deal with the construction of sequences of irreducible polynomials with coefficients in finite fields of even characteristic. We rely upon a transformation used by Kyuregyan in 2002, which generalizes the $Q$-transform employed previously by Varshamov and Garakov (1969) as well as by Meyn (1990) for the synthesis of irreducible polynomials. While in the iterative procedure described by Kyuregyan the coefficients of the initial polynomial of the sequence have to satisfy certain hypotheses, in the present paper these conditions are removed. We construct infinite sequences of irreducible polynomials of non-decreasing degree starting from any irreducible polynomial.
We deal with the construction of sequences of irreducible polynomials with coefficients in finite fields of even characteristic. We rely upon a transformation used by Kyuregyan in 2002, which generalizes the $Q$-transform employed previously by Varshamov and Garakov (1969) as well as by Meyn (1990) for the synthesis of irreducible polynomials. While in the iterative procedure described by Kyuregyan the coefficients of the initial polynomial of the sequence have to satisfy certain hypotheses, in the present paper these conditions are removed. We construct infinite sequences of irreducible polynomials of non-decreasing degree starting from any irreducible polynomial.
DOI : 10.1007/s10587-016-0253-2
Classification : 11R09, 11T55, 12E05
Keywords: finite field; irreducible polynomial; iterative construction 
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Ugolini, Simone. On an iterated construction of irreducible polynomials over finite fields of even characteristic by Kyuregyan. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 243-250. doi: 10.1007/s10587-016-0253-2

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