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arXiv · 1204.6692

Sequences of binary irreducible polynomials

Simone Ugolini
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Abstract

In this paper we construct an infinite sequence of binary irreducible polynomials starting from any irreducible polynomial $f_0 \in \F_2 [x]$. If $f_0$ is of degree $n = 2^l \cdot m$, where $m$ is odd and $l$ is a non-negative integer, after an initial finite sequence of polynomials $f_0, f_1, ..., f_{s}$ with $s \leq l+3$, the degree of $f_{i+1}$ is twice the degree of $f_i$ for any $i \geq s$.

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Simone Ugolini. 2012-09-01. Sequences of binary irreducible polynomials. https://doi.org/10.1016/j.disc.2013.08.011

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