In the
present paper, geometry of the Boolean space Bn in terms of Hausdorff distances between subsets and
subset sums is investigated. The main results are the algebraic and analytical
expressions for representing of classical figures in Bn and the functions of distances between them. In
particular, equations in sets are considered and their interpretations in
combinatory terms are given.
References
[1]
Nigmatulin, R.G. (1991) Complexity of Boolean Functions. Moscow, Nauka, 240 (in Russian).
[2]
McWilliams, F.J. and Sloane, N.J.A. (1977) The Theory of Error-Correcting Codes, Parts I and II. North-Holland Publishing Company, Amsterdam.
[3]
Leontiev, V.K. (2001) Selected Problems of Combinatorial Analysis. Bauman Moscow State Technical University, Moscow, 2001 (in Russian).
[4]
Leontiev, V.K. (2015) Combinatorics and Information. Moscow Institute of Physics and Technology (MIPT), Moscow, 2015 (in Russian).
[5]
Leontiev, V.K., Movsisyan, G.L. and Osipyan, A.A. (2014) Classification of the Subsets Bn, and the Additive Channels. Open Journal of Discrete Mathematics (OJDM), 4, 67-76.
[6]
Leontiev, V.K., Movsisyan, G.L., Osipyan, A.A. and Margaryan, Zh.G. (2014) On the Matrix and Additive Communication Channels. Journal of Information Security (JIS), 5, 178-191.
[7]
Leontiev, V.K., Movsisyan, G.L. and Margaryan, Zh.G. (2012) Constant Weight Perfect and D-Representable Codes. Proceedings of the Yerevan State University, Physical and Mathematical Sciences, 16-19.
[8]
Movsisyan, G.L. (1982) Perfect Codes in the Schemes Johnson. Bulletin of MSY, Computing Mathematics and Cybernetics, 1, 64-69 (in Russian).
[9]
Movsisyan, G.L. (2013) Dirichlet Regions and Perfect Codes in Additive Channel. Open Journal of Discrete Mathematics (OJDM), 3, 137-142.