Construction of irreducible polynomials using cubic transformation
The author shows that for all finite fields of characteristic \(>3\), there exists a polynomial \(f(x)\) of degree \(n\), each \(n\geq 1\), in \(F_q[X]\) which generates an infinite sequence of irreducible polynomials of degree \(3^in\) by iteration of the transformation \(f(x) \mapsto f(x^3-3x)\).
infinite sequence of irreducible polynomials
scientific article; zbMATH DE number 852849