Duality between bent functions and affine functions

A Boolean function in an even number of variables is called bent if it is at the maximal possible Hamming distance from the class of all affine Boolean functions. We prove that there is a duality between bent functions and affine functions. Namely, we show that affine function can be defined as a Boolean function that is at the maximal possible distance from the set of all bent functions.

► A Boolean function is bent if it is at the maximal distance from all affine functions.
► We prove that there is a duality between bent functions and affine functions.
► We show that affine functions can be defined as functions on the maximal distance from bent functions.