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

vol 66 / August, 2023

DOI 10.17586/0021-3454-2016-59-3-202-210

UDC 519.725


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

A. E. Chernyavskikh
A. F. Mozhaysky Military Space Academy, Department of Technologies and Means of Complex Processing and Transfer of Information in Automated Control Systems; Student

Read the full article 

Abstract. An algorithm for the generation of ternary Gordon—Mills—Welch (GMW) sequences and for determining the initial states of the shift registers, incorporated into the generation device, is developed. Ternary GMW-sequences, as well as binary, may be formed on the base of set of shift registers, which linear feedback are determined by coefficients of indivisible polynomials being the factors of testing polynomials of GMW-sequences. The main problem in the construction of devices generating ternary GMWsequences based on shift registers is absence in literature of algorithms of definition of their initial states. In accordance with the proposed algorithm the initial state of shift registers is determined by the decimation of the symbols of the base M-sequence, on which GMW-sequence is formed. Decimation index depends on the ratio of the degrees of the roots of polynomials-factors and roots of polynomial of the base M-sequence.
Keywords: ternary sequences of composite period, finite fields, indivisible and primitive polynomials, shift register with linear feedback



  1. Varakin L.E. Sistemy svyazi s shumopodobnymi signalami (Communication Systems with Noise-Like Signals), Moscow, 1985, 384 p. (in Russ.)
  2.  Ipatov V.P. Spread Spectrum and CDMA. Principles and Applications, Wiley, 2005, 400 р.
  3. Sverdlik M.B. Optimal'nye diskretnye signaly (Optimal Discrete Signals), Moscow, 1975, 200 p. (in Russ.)
  4. Meshkovskiy K.A., Krengel' E.I. Radiotekhnika, 1998, no. 5, pp. 25–28. (in Russ.)
  5. Stel'mashenko B.G., Taranenko P.G. Zarubezhnaya radioelektronika, 1988, no. 9, pp. 76–82. (in Russ.)
  6. Krengel' E. I. Tekhnika sredstv svyazi. Ser. TRS, 1979, no. 3, pp. 17–30. (in Russ.)
  7. Kalmykov V.V., Fedorov I.B., Yudachev S.S. Sistemy sotovoy i sputnikovoy svyazi (Systems of Cellular and Satellite Communication), Moscow, 2010, 280 p. (in Russ.)
  8. Varakin L.E., Shinakov Yu.S. (ed.) CDMA: proshloe, nastoyashchee, budushchee (CDMA: Last, Real, Future), Moscow, 2003, 608 p. (in Russ.)
  9. Yudachev S.S., Kalmykov V.V. "Nauka i obrazovanie" elektronnoe nauch.-tekhn. izdanie (Science and Education of Bauman MSTU), 2012, no. 1, /issue/264798.html. (in Russ.)
  10. Yudachev S.S. Elektronnyy nauch.-tekhn. zhurn. "Inzhenernyy vestnik" MGTU im. N. E. Baumana (Engineering Bulletin of Bauman MSTU), 2013, no. 1, pp. 531–540, (in Russ.)
  11. Alasmary W., Zhuang W. Ad Hoc Networks, 2010, pр. 1–9.
  12. Levanon N., Mozeson E. Radar signals, Chichester, John Wiley & Sons, 2005, 411 p.
  13. Prozorov D.E. Electrosvyaz, 2008, no. 8, pp. 48–51. (in Russ.)
  14. Prozorov D. E., Smirnov A. V., Balanov M. Yu. Vestnik of RSREU, 2015, no. 1(51), pp. 3–9. (in Russ.)
  15. Ipatov V.P. Periodicheskie diskretnye signaly s optimal'nymi korrelyatsionnymi svoystvami (Periodic Discrete Signals with Optimum Correlation Properties), Moscow, 1992, 152 p. (in Russ.)
  16. Golomb S.W. IEEE Transactions on Aerospace and Electronic Systems, 1992, no. 2(28), pp. 383–386.
  17. Golomb S.W., Gong G. Signal Design for Good Correlation for Wireless Communication, Criptography and Radar, Cambridge University Press, 2005, 438 p.
  18. Lie-Liang Yang, Hanzo L. Wireless Communications and Networking, 2003, no. 1, pp. 683–687.
  19. Leukhin A.N., Parsaev N.V. Radiotekhnika, 2009, no. 12, pp. 6–11. (in Russ.).
  20. Starodubtsev V.G. Izv. vuzov. Priborostroenie, 2012, no. 7(55), pp. 5–9. (in Russ.)
  21. Starodubtsev V.G. Izv. vuzov. Priborostroenie, 2013, no. 12(56), pp. 7–14. (in Russ.)
  22. Starodubtsev V.G. Izv. vuzov. Priborostroenie, 2015, no. 6(58), pp. 451–457. (in Russ.)