Comment on: Construction of irreducible polynomials using cube transformation by W. M. Chu (Q1361017)

The author points out that the cubic transformation considered by \textit{W. M. Chu} [Appl. Algebra Eng. Commun. Comput. 7, 15--19 (1996; Zbl 0869.11096)] is the case \(r=3\) of the more general transformation \(f(x)\mapsto f(D_r(x,1))\), where \(D_r\) denotes the familiar Dickson (Chebyshev) polynomial of the first kind. Such constructions of irreducible polynomials relate to ones based on \(f(x)\mapsto f(x^r)\). Further details are given in the author's Erlangen thesis (1993) [Darstellungen des algebraischen Abschlusses endlicher Körper and spur-kompatible Polynomfolgen, Friedrich-Alexander-Univ., Erlangen (1993; Zbl 0866.11071)].