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

Dmitry Khovratovich

Paper 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.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. The Russian version was submitted to the workshop on discrete mathematics in Russia in 2006
Keywords: boolean functions Hamming weight algebraic normal form coding theory
Contact author(s): diho @ rnt ru
History: 2006-05-30: received
Short URL: https://ia.cr/2006/180
License: CC BY

BibTeX

@misc{cryptoeprint:2006/180,
      author = {Dmitry Khovratovich},
      title = {Divisibility of the Hamming Weight by $2^k$ and Monomial Criteria for Boolean Functions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2006/180},
      year = {2006},
      url = {https://eprint.iacr.org/2006/180}
}

Paper 2006/180

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

Abstract

Metadata

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