FAKULTÄT FÜR

MATHEMATIK

Am 27. September 2022 trägt Dr. Alexandr Polujan im Mathematischen Forschungskolloquium des Instituts für Mathematik der Universität Rostock vor. Auf Einladung von Prof.in Dr. Gohar Kyureghyan spricht er über "Designs and Vectorial Bent Functions" vor.

Dr.  Alexandr Polujan besuchte vom September 11. - 17., 2022 den Workshop " The 7th International Workshop on Boolean Functions and their Applications (BFA)" in Balestrand, Norwegen und trug über das Thema "Towards the Classification of Quadratic Vectorial Bent Functions in 8 Variables" vor.

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.

Prof. Dr. Alexander Pott und Ali Ardalani besuchten vom Augusyt 1. - 5., 2022 den Workshop "The 10th International Workshop on Signal Design and its Applications in Communications (IWSDA'2022)" in University of Essex, Colchester, UK (online). Ali Ardalani trug über "A new Transformation for Costas Arrays" vor.

Das akzeptierte Paper befindet sich unter folgendem Link.