For a set of quadratic polynomials over a finite field, let be the (infinite) set of arbitrary compositions of elements in . In this paper we show that there are examples with arbitrarily large such that every polynomial in is irreducible. As a second result, when , we give an algorithm to determine whether all the elements in are irreducible, using only operations.
Cite this article
David Rodney Heath-Brown, Giacomo Micheli, Irreducible polynomials over finite fields produced by composition of quadratics. Rev. Mat. Iberoam. 35 (2019), no. 3, pp. 847–855DOI 10.4171/RMI/1072