Further Results on Niho Bent Functions
Lilya Budaghyan, Claude Carlet, Tor Helleseth, Alexander Kholosha, Sihem Mesnager · IEEE Transactions on Information Theory · 2012
This paper consists of two main contributions. First, the Niho bent function consisting of 2rexponents (discovered by Leander and Kholosha) is studied. The dual of the function is found and it is shown that this new bent function is not of the Niho type. Second, all known univariate representations of Niho bent functions are analyzed for their relation to the completed Maiorana-McFarland classM. In particular, it is proven that two families do not belong to the completed classM. The latter result gives a positive answer to an open problem whether the classHof bent functions introduced by Dillon in his thesis of 1974 differs from the completed classM.