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

vol 62 / April, 2019

DOI 10.17586/0021-3454-2018-61-3-240-248

UDC 519.725


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

V. M. Kuznetsova
A. F. Mozhaisky Military Space Academy, Department of Technologies and Means for Automation of Processing and Analysis of Space Systems Information; Student

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Abstract. Based on developed algorithm for generating Gordon — Mills — Welch sequences, a full list of testing polynomials for GMW-sequences with the period N = 511 is obtained. Binary GMW-sequences are formed on the basis of base M-sequence over finite fields with double expansion GF[(2m)n] and can be represented as a matrix of dimension [JxL]=[(2m–1)x(2m+1)]. A qualitative specifics of sequences with the period N = 511 consists in the fact that they are formed over a finite field GF[(23)3] and are presented in the form of a matrix of dimension [JxL]=[7x73], but not in the form of quasi-quadratic matrix of dimension [(2m–1)x(2m+1)]. Equivalent linear complexity of these sequences corresponds to the degree of the testing polynomial which can be represented as a product of three irreducible polynomials of the ninth degree. GMW-sequences with period N = 511 are formed using M-sequences of the same period. There are 48 primitive polynomials of the ninth degree in the field GF(29), the full list also contains 48 test polynomials for GMW-sequences. 
Keywords: sequences of composite period, finite fields, indivisible and primitive polynomials, equivalent linear complexity

  1. Ipatov V.P. Spread Spectrum and CDMA. Principles and Applications, Wiley, 2005, 400 р.
  2.  Vishnevskiy V.M., Lyakhov A.I., Portnoy S.L., Shakhnovich I.V. Shirokopolosnye besprovodnye seti peredachi informatsii (Broadband Wireless Networks of Information Transfer), Moscow, 592 р. (in Russ.)
  3.  Sklar B. Digital Communications: Fundamentals and Applications, Prentice-Hall, 2001.
  4.  Varakin L.E., Shinakov Yu.S., ed., CDMA: proshloe, nastoyashchee, budushchee (CDMA: Last, Real, Future), Moscow, 2003, 608 p. (in Russ.)
  5.  Ershen Wang, Shufang Zhang, Qing Hu. GPS Correlator Research and FPGA Implementation. Journal of System Simulation, 2008, vol. 20, рр. 3582–3585.
  6.  Golomb S.W., Gong G. Signal Design for Good Correlation for Wireless Communication, Criptography and Radar, Cambridge University Press, 2005, 438 p.
  7.  Ipatov V.P. Periodicheskie diskretnye signaly s optimal'nymi korrelyatsionnymi svoystvami (Periodic Discrete Signals with Optimum Correlation Properties), Moscow, 1992, 152 p. (in Russ.)
  8.  Prozorov D.E., Smirnov A.V., Balanov M.Yu. Vestnik of RSREU, 2015, no. 1(51), pp. 3–9. (in Russ.)
  9.  Golomb S.W. IEEE Transactions on Aerospace and Electronic Systems, 1992, March, no. 2(28), pp. 383–386.
  10.  Lie-Liang Yang, Hanzo L. Wireless Communications and Networking, 2003, no. 1, pp. 683–687.
  11.  Cho Chang-Min, Kim Ji-Youp, No Jong-Seon. IEICE Transactions on Communications, 2015, no. 7(E98), pp. 1268–1275.
  12.  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.)
  13.  Starodubtsev V.G. Journal of Instrument Engineering, 2012, no. 7(55), pp. 5–9.(in Russ.)
  14.  No Jong-Seon. IEEE Transactions on Information Theory, 1996, no. 1(42), pp. 260–262.
  15.  Chung H., No J.S. IEEE Transactions on Information Theory, 1999, no. 6(45), pp. 2060–2065.
  16.  Starodubtsev V.G. Journal of Instrument Engineering, 2013, no. 12(56), pp. 7–14.(in Russ.)
  17.  Starodubtsev V.G. Journal of Instrument Engineering, 2015, no. 6(58), pp. 451–457.(in Russ.)
  18.  Starodubtsev V.G., Popov A.M. Journal of Instrument Engineering, 2017, no. 4(60), pp. 318–330.
  19.  Peterson W.W.  & Weldon E.J. Error-Correcting Codes, Second Edition, MIT Press, 1972, 560 p.