Sequences of binary irreducible polynomials

In this paper we construct an infinite sequence of binary irreducible polynomials starting from any irreducible polynomial f0∈F2[x]. If f0 is of degree n=2l⋅m, where m is odd and l is a nonnegative integer, after an initial finite sequence of polynomials f0,f1,…,fs, with s≤l+3, the degree of fi+1 is twice the degree of fi for any i≥s.