Classes of Quadratic APN Trinomials and Hexanomials and Related Structures

A method for constructing differentially 4-uniform quadratic hexanomials has been recently introduced by J. Dillon. We give various generalizations of this method and we deduce the constructions of new infinite classes of almost perfect nonlinear quadratic trinomials and hexanomials from F
_22m
to F
_22m
. We check for m = 3 that some of these functions are CCZ-inequivalent to power functions.