## Cryptology ePrint Archive: Report 2006/180

Divisibility of the Hamming Weight by $2^k$ and Monomial Criteria for Boolean Functions

Dmitry Khovratovich

Abstract: 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 $2^k$. 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 $2^k, \,k>1$, it is necessary and sufficient to know its algebraic normal form accurate to an additive constant.

Category / Keywords: boolean functions, Hamming weight, algebraic normal form, coding theory

Publication Info: The Russian version was submitted to the workshop on discrete mathematics in Russia in 2006