Construction of a Reversible Full-cycle Transformation in a Threshold Basis
( Pp. 36-41)

The article describes a class of full-cycle transformations in the threshold basis, defined by matrices of coefficients of linear forms, and proves that the definition of the inverse transformation is carried out using a system of threshold functions, the coefficients of which form the transposed matrix with respect to the original one.

Nikonov V.G., Zobov A.I. Construction of a Reversible Full-cycle Transformation in a Threshold Basis. Computational Nanotechnology. 2023. Vol. 10. No. 2. Pp. 36–41. (In Rus.) DOI: 10.33693/2313-223X-2023-10-2-36-41. EDN: BHHIVN

Zobov A.I., Nikonov V.G. On the possibility of applying fractal models in the construction of information security systems. Comp. nanotechnol. 2017. No. 1. Pp. 39–49. (In Rus.)
Logachev O.A., Salnikov A.A., Smyshlyaev S.V., Yashchenko V.V. Boolean functions in coding theory and cryptography. 2nd ed., add. Moscow: MCCME, 2012. 584 p.
Logachev O.A., Fedorov S.N., Yashchenko V.V. Boolean functions as points on the hypersphere in Euclidean space. Discrete Mathematics. 2018. Vol. 30. No. 1. Pp. 39–55. (In Rus.)
Nikonov V.G., Sarantsev A.V. Methods for compact implementation of bijective mappings defined by regular systems of identical Boolean functions. Bulletin of the Peoples’ Friendship University of Russia. Series: Applied Mathematics and Industrial Mathematics. 2003. Vol. 2. No. 1. Pp. 94–105. (In Rus.)
Yablonsky S.V. Introduction to discrete mathematics: textbook for universities. 2nd ed., rev. and add. Moscow: Nauka; Chief Ed. of Phys.-Math. Lit. 384 p.

substitution, threshold function, full cycle.