New ternary binomial bent functions
Tor Helleseth, Alexander Kholosha · 2016
The ternary function f(x) mapping F34kto F3and given by f(x) = Tr4k(a1x2(3k+1)+ a2x(3k+1)2), where a1is a nonsquare in F34kand a2is defined explicitly by a1, is proven to be a regular bent function of degree four belonging to the completed Maiorana-McFarland class. The proof is based on a new criterion that allows checking bentness by analyzing first- and second-order derivatives.