CryptoDB
Divisibility of the Hamming Weight by $2^k$ and Monomial Criteria for Boolean Functions
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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. |
BibTeX
@misc{eprint-2006-21673, title={Divisibility of the Hamming Weight by $2^k$ and Monomial Criteria for Boolean Functions}, booktitle={IACR Eprint archive}, keywords={boolean functions, Hamming weight, algebraic normal form, coding theory}, url={http://eprint.iacr.org/2006/180}, note={The Russian version was submitted to the workshop on discrete mathematics in Russia in 2006 diho@rnt.ru 13293 received 25 May 2006}, author={Dmitry Khovratovich}, year=2006 }