From February 3 to March 1, 2020, Alexander Kutsenko and Alexey Oblaukhov trained at the Selmer Center in Secure Communication research center Of the University of Bergen (Norway). During this time, joint research was carried out, and three times spoke at the laboratory's seminar:
13.02.2020-A. Kutsenko, "Self-dual bent functions: characterization and metric properties". Known properties of self-dual bent functions are considered. The obtained metric properties are described: the minimum Hamming distance between self-dual bent functions, and the spectrum of Hamming distances between functions from the Mayoran-Macfarland class. The metric regularity is proved and the metric complement of the set of self-dual bent functions is found.
20.02.2020-A. Kutsenko, "The group of automorphisms of the set of self-dual bent functions". The results obtained for isometric mappings of a set of self-dual benp functions are presented. It is proved that the automorphism groups of sets of self-dual and anti-self-dual bent functions coincide. The group of automorphisms of the set of self-dual bent functions is fully described.
27.02.2020 - A. Oblaukhov, "Metric regularity and metric complements in the Boolean cube". We present the results obtained that affect the properties of metric additions of subsets of a Boolean cube. A General view of the metric complement of a linear subspace of a Boolean cube is found. A lower estimate for the power of the maximum metrically regular set is obtained. The metric regularity of the reed-Maller codes RM(k, m) is proved for the case k>=m−3.