Systematic Methods of Constructing Bent Functions and 2-Rotation Symmetric Bent Functions

In this paper, we first present two systematic constructions of bent functions by modifying the truth tables of Rothaus's bent function and Maiorana-McFarland's bent function respectively. The number of the newly constructed bent functions by modifying the truth table of Rothaus's bent function is also determined. The methods of constructing self-dual bent functions are then given after the dual functions of these bent functions being determined. Finally, as an application, two constructions of 2-rotation symmetric bent functions are presented in this paper.