RESULTS ON BENT FUNCTIONS

In this paper, we present three results on bent functions: a construct ion, a restriction and a characterization. Starting with a single bent function, in a simple but very effective way, the construction produc es a large number of new bent functions in the same number of variable s. The restriction imposes new conditions on tile directional derivati ves of bent functions. Certain non-existence results that were previou sly obtained through computer starch follow easily from these conditio ns. The characterization describes bent functions as certain solutions of a system of quadratic equations. Interesting new properties of ben t functions are obtained using the characterization. (C) 1997 Academic Press.