Divisibility of the Hamming Weight by 2k and Monomial Criteria for Boolean Functions
In this paper we consider the notions of the Hamming weight and the algebraic normal form. We solve an open problem devoted to checking divisibility of the weight by 2. We generalize the criterion for checking the evenness of the weight in two ways. Our main result states that for checking whether the Hamming weight of f is divisible by 2, k > 1, it is necessary and sufficient to know its algebraic normal form accurate to an additive constant.