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Formation of Ternary Sequences with High Structural Secrecy in Digital Information Trans-fer Systems

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An algorithm for determining initial states of shift registers included in the Gordon-Mills-Welch (GMW) ternary sequence generation device with the period of N = 728 is presented. The algorithm is based on comparison of the initial states obtained by solving the system of linear equations in the finite fields and the states determined by decimation of characters of the basic M-sequence. Ternary M-sequences and GMW-sequences have the same two-level periodic autocorrelation function, but different structural secrecy, characterized by equivalent linear complexity. The GMW-sequence is formed using a basic M-sequence with a similar period when it is presented in the form of quasi-square matrix. It is shown that for each of the 48 primitive polynomials in the finite field GF (36), three GMW-sequences can be formed. For binary GMW sequences, the initial states of the shift registers are formed by decimating the symbols of the basic M-sequence, presented in canonical form, by decimation indices corresponding to the roots of indivisible polynomial factor factors. For ternary GMW sequences, the individual summable components have an additional half-period shift of the base M-sequence. It is argued that the obtained results can be used for generating broadband non-binary signals in digital information transmission systems.

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