Results on Bent Functions

Xiang-dong Hou, Philippe Langevin
1997 Journal of combinatorial theory. Series A  
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 search follow easily from these conditions. The
more » ... aracterization describes bent functions as certain solutions of a system of quadratic equations. Interesting new properties of bent functions are obtained using the characterization. 1997 Academic Press [1 5] by Carlet, [6] by Carlet and Guillot, [8] by Dobbertin, [10] by Kumar, Scholtz, Welch, and [11] by Langevin on constructions, characterizations, and generalizations of bent functions. Also see [9] by Hou on cubic bent functions. Despite extensive study, many questions about bent functions remain open. The ultimate goal of classifying bent functions under the action of the general affine group seems to be out of reach for
doi:10.1006/jcta.1997.2804 fatcat:d42yzmuzfzc2ldwg43dpe3lwy4