2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229598We describe several families of permutation polynomials obtained using functions with linear translators.An extension of the paper "Remarks on a family of permutation polynomials":Section 2 is expanded, Sections 3,4 are new, several typos are correctedNumber TheoryCombinatorics11T06; 11T71Constructing permutations of finite fields via linear translatorstext