More constructions of APN and differentially 4-uniform functions by concatenation

We study further the method of concatenating the outputs of two functions for designing an APN or a differentially 4-uniform (n, n)-function for every even n. We deduce several specific constructions of APN or differentially 4-uniform (n, n)-functions from APN and differentially 4-uniform (n/2, n/2)-functions. We also give a construction of quadratic APN functions which includes as particular cases a previous construction by the author and a more recent construction by Pott and Zhou.