Cubic bent functions outside the completed Maiorana-McFarland class
Alexandr A. Polujan, Alexander Pott · Designs Codes and Cryptography · 2020
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 $$n\ge 10$$ n ≥ 10 . Moreover, we show that for almost all values of n, these functions can simultaneously be homogeneous and have no affine derivatives.