Geodesic
Constructing substitutions on the basis of threshold functions of multivalued logic
Prikladnaâ diskretnaâ matematika, no. 2 (2016), pp. 20-32.

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An algorithm for building one-to-one mappings (substitutions) with the help of coordinate threshold $k$-valued logic functions is presented. The algorithm includes a geometric way of generating balanced threshold functions and two ways to produce substitutions from these functions – by forming triangular systems and by algorithmic searching. Results of experimental testing the algorithms are given.
Keywords: threshold functions, multiple-valued logic, balanced functions, regular systems. 
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D. A. Soshin. Constructing substitutions on the basis of threshold functions of multivalued logic. Prikladnaâ diskretnaâ matematika, no. 2 (2016), pp. 20-32. http://geodesic.mathdoc.fr/item/PDM_2016_2_a1/

[1] Nikonov V. G., Sarantsev A. V., “Methods of compact realization of bijective mappings proposed by regular systems of one-type Boolean functions”, Vestnik RUDN. Ser. Prikladnaya i Komp'yuternaya Matematika, 2:1 (2003), 94–105 (in Russian)

[2] Nikonov V. G., Sarantsev A. V., “The construction and classification of the regular systems of one-type functions”, Proc. XXXI Int. conf. “Informatsionnye tekhnologii v nauke, obrazovanii, telekommunikatsii i biznese”, v. 5, Moscow, 2004, 173–174 (in Russian)

[3] Nikonov V. G., Sidorov E. S., “About the possibility of one-to-one mappings representation by the quasi-hadamard matrixes”, Vestnik Moskovskogo Gosudarstvennogo Universiteta Lesa – Lesnoy Vestnik, 2009, no. 2(65), 155–157 (in Russian)

[4] Nikonov V. G., Soshin D. A., “The geometric method for constructing a balanced $k$-valued threshold functions and construction of substitutions based on them”, Obrazovatel'nye Resursy i Tekhnologii, 2014, no. 2(5), 76–80 (in Russian)

[5] Alferov A. P., Zubov A. Yu., Kuz'min A. S., Cheremushkin A. V., Basics of Cryptography, Gelios ARV Publ., Moscow, 2001 (in Russian)

[6] Dertouzos M., Threshold Logic, Mir Publ., Moscow, 1967 (in Russian)

[7] Efimov N. V., Rozendorn E. R., Linear Algebra and Multidimensional Geometry, Nauka Publ., Moscow, 1970 (in Russian) | MR

[8] Glukhov M. M., Shishkov A. B., Mathematical Logic. Discrete Functions. Algorithms Theory, Lan' Publ., Moscow, 2012