Several New Infinite Families of Bent Functions and Their Duals

Bent functions are optimal combinatorial objects. Since their introduction, substantial efforts have been directed toward their study in the last three decades. A complete classification of bent functions is elusive and looks hopeless today, therefore, not only their characterization, but also their generation are challenging problems. This paper is devoted to the construction of bent functions. First, we provide several new effective constructions of bent functions, self-dual bent functions, and antiself-dual bent functions. Second, we provide seven new infinite families of bent functions by explicitly calculating their dual.