Sequences of binary irreducible polynomials

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 $s\le l+3$, the degree of $f_{i+1}$ is twice the degree of $f_i$ for any $i\ge s$.

7 pages, minor adjustments

References in corpus (1)

• Graphs associated with the map $x\mapsto x+x^{-1}$ in finite fields of characteristic two

Cited by in corpus (4)

• Sequences of irreducible polynomials without prescribed coefficients over odd prime fields
• Construction of irreducible polynomials through rational transformations
• On the construction of irreducible polynomials over finite fields via prime degree endomorphisms of elliptic curves
• Sequences of irreducible polynomials without prescribed coefficients over finite fields of even characteristic