Linear codes and incidence structures of bent functions and their generalizations

In this paper, we consider further applications of (n,m)-functions for the construction 2-designs. For instance, provide a new application extended Assmus-Mattson theorem, by showing that linear codes certain APN functions with classical Walsh spectrum support With result, give several sufficient conditions an function to be CCZ-inequivalent quadratic one. On other hand, use and combinatorial designs in order study important properties (n,m)-functions. particular, characterization Boolean bent means 2-transitivity its automorphism group. Finally, design-theoretic (n,m)-plateaued (n,m)-bent coding-theoretic as well interpretation extendability problem functions.