Abstract
In this paper we construct infinite sequences of monic irreducible polynomials with coefficients in odd prime fields by means of a transformation introduced by Cohen in 1992. We make no assumptions on the coefficients of the first polynomial \(f_0\) of the sequence, which belongs to \(\mathbf{F}_p [x]\), for some odd prime \(p\), and has positive degree \(n\). If \(p^{2n}-1 = 2^{e_1} \cdot m\) for some odd integer \(m\) and non-negative integer \(e_1\), then, after an initial segment \(f_0, \dots , f_s\) with \(s \le e_1\), the degree of the polynomial \(f_{i+1}\) is twice the degree of \(f_i\) for any \(i \ge s\).
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The author is grateful to the anonymous Reviewer for the thoughtful comments and remarks, which contributed to improve the quality of the paper.
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Communicated by G. Mullen.
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Ugolini, S. Sequences of irreducible polynomials without prescribed coefficients over odd prime fields. Des. Codes Cryptogr. 75, 145–155 (2015). https://doi.org/10.1007/s10623-013-9897-1
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DOI: https://doi.org/10.1007/s10623-013-9897-1