ISSN 0021-3454 (print version)
ISSN 2500-0381 (online version)

vol 63 / August, 2020

DOI 10.17586/0021-3454-2020-63-5-405-416

UDC 519.725

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

V. G. Starodubtsev
Multiservice Nets and Telecommunications, Ltd., St. Petersburg; Head of Department

V. V. Tkachenko
A. F. Mozhaisky Military Space Academy;

E. A. Bobrova
A. F. Mozhaisky Military Space Academy;

Abstract. 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.
Keywords: pseudorandom sequences, finite fields, indivisible and primitive polynomials, structural secrecy, decimation, shift registers



  1. Vishnevskij V.M., Lyahov A.I., Portnoj S.L., Shahnovich I.V. Shirokopolosnye besprovodnye seti peredachi informacii (Broadband Wireless Data Transmission Network), Moscow, 2005, 592 p. (in Russ.)
  2. Sklar B. Digital Communications: Fundamentals and Applications, Prentice Hall, 2001, 1079 р.
  3. Ipatov V.P. Spread Spectrum and CDMA. Principles and Applications, NY, John Wiley and Sons Ltd., 2005, 488 р.
  4. Varakin L.E. and Shinakov Yu.S., ed., CDMA: proshloe, nastoyashchee, budushchee (CDMA: Past, Present, Future), Moscow, 2003, 608 p. (in Russ.)
  5. Golomb S.W., Gong G. Signal Design for Good Correlation for Wireless Communication, Cryptography and Radar, Cambridge University Press, 2005, 438 p.
  6. Chung H.B., No J.S. IEEE Transactions on Information Theory, 1999, no. 6(45), pp. 2060–2065.
  7. Rizomiliotis P., Kalouptsidis N. IEEE Transactions on Information Theory, 2005, vol. IT–51, pp. 1555–1563.
  8. Ipatov V.P. Periodicheskie diskretnye signaly s optimal'nymi korrelyacionnymi svojstvami (Periodic Discrete Signals with Optimum Correlation Properties), Moscow, 1992, 152 p. (In Russ.).
  9. No Jong-Seon. IEEE Transactions on Information Theory, 1996, no. 1(42), pp. 260–262.
  10. Starodubtsev V.G., Chernjavskih A.E. Journal of Instrument Engineering, 2016, no. 3(59), pp. 201–210. (in Russ.)
  11. Tsankov T., Trifonov T., Staneva L. Journal Scientific & Applied Research, 2013, vol. 4, pp. 80–87.
  12. Starodubtsev V.G. Trudy SPIIRAN (SPIIRAS Proceedings), 2019, no. 4(18), pp. 912–948. (in Russ.)
  13.  Lee Wijik, Kim Ji-Youp, No J.S. IEICE Transactions on Communications, 2014, no. 1(E97-B), pp. 2311–2315.
  14. Cho Chang-Min, Kim Ji-Youp, No J.S. IEICE Transactions on Communications, 2015, no. 7(E98), pp. 1268–1275.
  15. Tasheva Z. Journal Scientific & Applied Research, 2014, vol. 2, pp. 17–26.
  16. Xia Y., Chen S. IEEE Transactions on Information Theory, 2012, no. 9(58), pp. 6037–6046.
  17. Helleseth T., Kumar P.V., Martinsen H. Designs, Codes and Cryptography, 2001, no. 2(23), pp. 157–166.
  18. Tang X.H., Pingzhi Z.F. IEEE Transactions on Information Theory, 2001, no. 4(47), pp. 1644–1649.
  19. Starodubtsev V.G., Tkachenko V.V., Malysheva E.A. Izvestiya Tulskogo gosudarstvennogo universiteta. Tekhnicheskie nauki (Proceedings of Tula State University. Technical science), 2019, no. 6, pp. 192–203 (in Russ.)
  20. Starodubtsev V.G., Borod'ko D.N., Myshko V.V. Aviakosmicheskoe priborostroenie (Aerospace Instrumentation), 2018, no. 5, pp. 3–15 (in Russ.)