Results on bent functions

摘要

In this paper, we present three results on bent functions: a construction, a restriction and a characterization. Starting with a single bent function, in a simple but very effective way, the construction produces a large number of new bent functions in the same number of variables. The restriction imposes new conditions on the directional derivatives of bent functions. Certain non-existence results that were previously obtained through computer starch follow easily from these conditions. The characterization describes bent functions as certain solutions of a system of quadratic equations. Interesting new properties of bent functions are obtained using the characterization. (C) 1997 Academic Press.