Sequences of binary irreducible polynomials

In this paper we construct an infinite sequence of binary irreducible polynomials starting from any irreducible polynomial f 0 ∈ F 2 [ x ] . If f 0 is of degree n = 2 l ⋅ m , where m is odd and l is a nonnegative integer, after an initial finite sequence of polynomials f 0 , f 1 , … , f s , with s ≤ l + 3 , the degree of f i + 1 is twice the degree of f i for any i ≥ s .