Email this article On the Existence, Method of Construction and Some Properties of (n - 2)-Structured Matrices Generating Bijective Transformations
- Authors: Kononov S.A.1
-
Affiliations:
- Secure Information Technology Assistance Foundation
- Issue: Vol 9, No 1 (2022)
- Pages: 93-105
- Section: Articles
- URL: https://journal-vniispk.ru/2313-223X/article/view/147110
- DOI: https://doi.org/10.33693/2313-223X-2022-9-1-93-105
- ID: 147110
Cite item
Open Access
Access granted
Subscription Access
Abstract
The article considers a new type of matrices that define bijective coordinate-threshold mappings - (n - 2)- structured matrices. It is proved that different matrices define different transformations, all (n - 2)-structured matrices of order 4 are described. For an arbitrary n ∈ ℕ, n classes of (n - 2)-structured matrices are specified, it is proved that the transformations specified by these matrices generate the group S2 S2n - 1. It is shown that the matrix transposed to the given one generates the inverse transformation.
Full Text
##article.viewOnOriginalSite##About the authors
Sergey A. Kononov
Secure Information Technology Assistance Foundation
Email: cononovsa@yandex.ru
Moscow, Russian Federation
References
- Belevitch V. Theorem of 2n terminal networks with application to conference telephony // Electrical Communication. 1950. Vol. 26. Pp. 231-244.
- Goethals J.M., Seidel J.J. Orthogonal matrices with zero diagonal // Canadian Journal of Mathematic. 1967. Vol. 19. Pp. 1001-1010.
- Burdelev A.V. Questions of independence threshold equiprobable Boolean functions. Forestry Bulletin. 2009. Vol. 3. Pp.116-119. (In Rus.)
- Burdelev A.V. Simplification of criterion Huffman for monotonous self-dual Boolean functions. Forestry Bulletin. 2010. No. 6. Pp. 178-183. (In Rus.)
- Glukhov M.M., Zubov A.Y. About lengths of the symmetric and alternating permutation groups via the systems of various generators. Mathematical Problems of Cybernetics. 1999. No. 8. Pp. 5-32. (In Rus.)
- Gluhov M.M. On numerical parameters associated with the definition of finite groups by systems of generating elements. Papers on Discrete Mathematics. 1997. Vol. 1. Pp. 43-66. (In Rus.)
- Glukhov M.M., Elizarov V.P., Nechaev A.A. Algebra. Moscow: Lan, 2015.
- Dertouzos М.L. Threshold logic: A synthesis approach. Cambridge, Massachusetts: MIT Press, 1965.
- Nikonov V.G., Zobov A.I. About possibility of using fractal models in data security system construction. Computantional Nanotechnology. 2017. No. 1. Pp. 39-48. (In Rus.)
- Nikonov V.G., Litvinenko V.S. Geometrical approach to the argumentum of bijection of one coordinate-threshold reflection. Computantional Nanotechnology. 2015. No. 1. Pp. 26-31. (In Rus.)
- Nikonov V.G., Litvinenko V.S. About bijectivity of transformations determined by quasi-hadamard matrixes. Computantional Nanotechnology. 2016. No. 1. Pp. 6-13. (In Rus.)
- Nikonov V.G, Sidorov Е.С. About the possibility of one-to-one mappings’ representation by the quasi-hadamard matrixes. Forestry Bulletin. 2009. No. 2. Pp. 155-158. (In Rus.)
- Pogorelov B.A. Permutation group theory. Moscow, 2019.
- Hall M. The theory of groups. Moscow, 1962.
Supplementary files
