Spectral and nonlinear properties of the complete quaternary code

Abstract

The current stage of development of information technologies is characterized by the active introduction of the functions of many-valued logic. In particular, many-valued logic functions are used in cryptography to build highquality cryptographic primitives with a high level of nonlinearity. This circumstance determines the need for more detailed research of the nonlinearity of the complete codes of functions of many-valued logic. Because of the possibility of representing constructions of almost all modern ciphers by 4-functions, they occupy a special place among other q values in the research of the level of nonlinearity. This paper presents a universal method for calculating the possible absolute values of the Vilenkin-Chrestenson transform coefficients of many-valued logic functions. This method is applied to 4-functions of length N = 4 and N = 16. As a result, 5 spectral classes of vectors of length N = 4, and 36 spectral classes of vectors of length N = 16 were discovered, each of which has a unique elementary structure, and, accordingly, the certain value of nonlinearity. Because of the dependence of such a fundamental concept of MC-CDMA technology as the Peak-to-Average Power Ratio of the applied signals and their spectral properties, the results obtained can also be used to calculate the maximum cardinality values of constant amplitude codes constructed based on many-valued logic functions.