Cubic bent functions outside the completed Maiorana-McFarland class

Alexandr Polujan; Alexander Pott

doi:10.1007/s10623-019-00712-y

paper

Cubic bent functions outside the completed Maiorana-McFarland class

arXiv:1908.11271 · doi:10.1007/s10623-019-00712-y

Abstract

In this paper we prove that in opposite to the cases of 6 and 8 variables, the Maiorana-McFarland construction does not describe the whole class of cubic bent functions in $n$ variables for all $n \geq 10$ . Moreover, we show that for almost all values of $n$ , these functions can simultaneously be homogeneous and have no affine derivatives.