From February 3 to March 1, 2020, Alexander Kutsenko and Alexey Oblaukhov had an internship at the Selmer Center in Secure Communication Research University of Bergen (Norway). During this time, joint scientific research was conducted, and the following presentations at the seminar organized by the host laboratory were made:
13.02.2020 Self-dual bent functions: characterization and metrical properties by A. Kutsenko. Known properties of self-dual bent functions are considered. The obtained metric properties are described: the minimum Hamming distance between self-dual bent functions, 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 The group of automorphisms of the set of self-dual bent functions by A. Kutsenko. The obtained results on isometric mappings of the set of self-dual bent functions are presented. It is proved that the automorphism groups of the sets of self-dual and anti-self-dual bent functions coincide. The automorphism group of the set of self-dual bent functions is completely described.
27.02.2020 Metric complements and metric regularity in the Boolean cube by A. Oblaukhov. The results are presented that affect the properties of metric complements of subsets of a Boolean cube. The general form of the metric complement of the linear subspace of a Boolean cube is found. A lower bound on the cardinality of a maximal metrically regular set is obtained. The metric regularity of the Reed-Muller codes RM(k,m) for the case 办鈮鈭�3 is proved.
