Cubic Maiorana–McFarland bent functions with no affine derivative
Bimal Mandal, Sugata Gangopadhyay, Pantelimon Stănică · International Journal of Computer Mathematics Computer Systems Theory · 2017
A class of cubic Maiorana–McFarland () bent functions having no affine derivative was constructed by Canteaut and Charpin [ Decomposing bent functions, IEEE Trans. Inform. Theory 49(8) (2003), pp. 2004–2019], thereby solving an open problem posed by Hou [Cubic bent functions, Discrete Math. 189 (1998), pp. 149–161]. The goal of the paper is twofold: we construct two classes of cubic bent functions with no affine derivative and show their mutual affine inequivalence.