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Mat. Vopr. Kriptogr., 2016, Volume 7, Issue 3, Pages 73–92 (Mi mvk197)  

On a method for constructing low-weight Boolean functions without majorants of the given number of variables

P. V. Roldugin

Moscow State University of Information Technologies, Radioengineering and Electronics, Moscow

Abstract: The problem of constructing Boolean functions without majorants of $k$ variables is reduced to the construction of a set $M$ of Boolean functions of $k-1$ variables such that for any different vectors $\overline\beta_1,…,\overline\beta_k\in V_{k-1}$ and for any $\alpha_1,…,\alpha_k\in\{0,1\}$ there exists a function $f\in M\colon f(\overline\beta_1)=\alpha_1,…,f(\overline\beta_k)=\alpha_k$. This approach permits to construct functions f of small weight having no $k-1$ variable majorants. Several families of such Boolean functions $f$ are constructed.

Key words: Boolean functions, majorants, Boolean matrices.

DOI: https://doi.org/10.4213/mvk197

Full text: PDF file (258 kB)
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Bibliographic databases:

Document Type: Article
UDC: 519.719.2+519.712
Received 20.IV.2014

Citation: P. V. Roldugin, “On a method for constructing low-weight Boolean functions without majorants of the given number of variables”, Mat. Vopr. Kriptogr., 7:3 (2016), 73–92

Citation in format AMSBIB
\Bibitem{Rol16}
\by P.~V.~Roldugin
\paper On a~method for constructing low-weight Boolean functions without majorants of the given number of variables
\jour Mat. Vopr. Kriptogr.
\yr 2016
\vol 7
\issue 3
\pages 73--92
\mathnet{http://mi.mathnet.ru/mvk197}
\crossref{https://doi.org/10.4213/mvk197}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3588375}
\elib{http://elibrary.ru/item.asp?id=28931396}


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