Upper bounding the number of bent functions using 2-row bent rectangles

Abstract

Using the representation of bent functions (maximum nonlinear functions) by bent rectangles, that is, special matrices with restrictions on columns and rows, we obtain herein an upper bound on the number of bent functions that improves the previously known bounds in a practical range of dimensions. The core of our method is the following fact based on the recent observation by V. Potapov (arXiv:2107.14583): a 2-row bent rectangle is completely determined by one of its rows and the remaining values in slightly more than half of the columns.