Construction of bent functions of 2k variables from a basis of F22k

Starting with a basis of F22k, we define some sets in F22k that are the supports of bent functions of 2k variables. We also establish some results in order to count the number of bent functions we can construct, and we provide a complete classification of all bases of F22k (for k = 2) providing the same supports of bent functions.This work was partially supported by Spanish grants MTM2008-06674-C02-01 and MTM2011-24858 of the Ministerio de Ciencia e Innovación of the Gobierno de España and ACOMP/2010/039 and ACOMP/2011/005 of the Generalitat Valenciana