Neues Paper von Alexandr Polujan und Alexander Pott
Das folgende Paper wurde kürzlich im Journal "Discrete Mathematics" veröffentlicht.
Linear codes and incidence structures of bent functions and their generalizations.
Discrete Mathematics, Volume 346, Issue 1, January 2023, 113157
Wilfried Meidl, Alexandr Polujan, Alexander Pott
Abstract
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 certain APN functions with the classical Walsh spectrum support 2-designs.
With this result, we give several sufficient conditions for an APN function with the classical Walsh spectrum to be CCZ-inequivalent to a quadratic one.
On the other hand, we use linear codes and combinatorial designs in order to study important properties of (n,m)-functions.
In particular, we provide a characterization of a quadratic Boolean bent function by means of the 2-transitivity of its automorphism group.
Finally, we give a new design-theoretic characterization of -plateaued and -bent functions and provide a coding-theoretic as well as a design-theoretic interpretation of the extendability problem for (n,m)-bent functions.