Linear codes and incidence structures of bent functions and their generalizations

12/12/2020

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by   Wilfried Meidl, et al.

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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.