Some general properties of modified bent functions through addition of indicator functions

摘要

Properties of a secondary bent function construction that adds the indicator of an affine subspace of arbitrary dimension to a given bent function in n variables are obtained. Some results regarding normal and weakly normal bent functions are generalized. An upper bound for the number of generated bent functions is proven. This bound is attained if and only if the given bent function is quadratic. In certain cases, the addition of the indicator of an m-dimensional subspace, for different m, will not generate bent functions. Such examples are presented for any even n = 10. It is proven that there exists an infinite family of Maiorana-McFarland bent functions such that the numbers of generated bent functions differ for the bent function and its dual function.