The class of 1-balanced functions and the complexity of its realization (Q1814332)

A classification of \(n\)-variables Boolean functions is proposed according to the distribution of their unit values on the \(n\)-dimensional cube. A Boolean function is said to be \(\ell\)-balanced if the unit value vertices numbers of each two equal dimension subcubes differ no more than \(\ell\). The class of 1-balanced functions is described and asymptotic estimate of its complexity is given.