  In this paper we consider further applications of $(n,m)$-functions for the
construction of 2-designs. For instance, we provide a new application of the
extended Assmus-Mattson theorem, by showing that linear codes of APN functions
with the classical Walsh spectrum support 2-designs. On the other hand, we use
linear codes and combinatorial designs in order to study important properties
of $(n,m)$-functions. In particular, we give a new design-theoretic
characterization of $(n,m)$-plateaued and $(n,m)$-bent functions and provide a
coding-theoretic as well as a design-theoretic interpretation of the
extendability problem for $(n,m)$-bent functions.
