  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 $i \geq s$.
