On two open problems on the normality of bent functions
Alexandr Polujan, Luca Mariot, Stjepan Picek · Discrete Applied Mathematics · 2024
Non-normal Boolean bent functions are one of the least understood classes of bent functions, and only a few difficult-to-find examples of such functions are known. In this paper, we consider the following two open problems on the normality of bent functions: 1. Do non-normal bent functions in 8 variables and degree 4 exist? 2. Do non-normal bent functions in the PS − ∖ PS a p class exist? We solve both of these problems by finding among the known PS bent functions in n = 8 variables a non-normal bent function in the PS − ∖ PS a p class.