Abstract. An analysis of periodic cross-correlation functions (PCCF) of M-sequences (MS) and Gordon-Mills-Welch sequences (GMWS), which have a two-level autocorrelation function, is presented. A higher structural secrecy of GMWS as compared with the MS determines the preference for the use of GMWS in digital information transmission systems (DITS) subject to increased confidentiality requirements. An algorithm for formation of preferred pairs of GMWS and their definitions for periods N = 63 and N = 255 are developed. Mathematical apparatus of the theory of finite fields, linear algebra and correlation analysis are used in the research. Values of PCCF of various pairs of MS and GMWS are obtained for periods N = 63 and N = 255. It is shown that GMWS, forming preferred pairs, are formed based on MS, also forming preferred pairs. The obtained results can be used in the formation of spread-spectrum signals in the noise-proof DITS, as well as in the synthesis of signal systems that allow an analytical representation in finite fields.

Keywords: pseudorandom sequences, preferred pairs, correlation function, structural secrecy, indivisible and primitive polynomials, finite fields

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