A further study on the construction methods of bent functions and self-dual bent functions based on Rothaus's bent function

Bent functions are maximally nonlinear Boolean functions. They are important functions introduced by Rothaus and studied firstly by Dillon and next by many researchers for more than four decades. A systematic construction method of bent functions by modifying the support of Rothaus's bent function was given in Su (IEEE Trans Inf Theory 66(5):3277-3291, 2020). In this paper, we give a further study on that construction method. Two more flexible construction methods of bent functions by modifying the support of Rothaus's bent function are given respectively. The newly constructed bent functions contain the result in Su (2020), which is simply a special subclass of the newly constructed bent functions. The dual functions of these bent functions are determined. The methods of constructing self-dual bent functions are given. And the numbers of the newly constructed bent functions are also presented.