Windmill Generators A generalization and an observation of how many there are

  • B. J. M. Smeets
  • W. G. Chambers
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 330)


The windmill technique has several practical advantageous over other techniques for high-speed generation or blockwise generation of pn-sequences. In this paper we generalize previous results by showing that if f(t)=α(t v) − β(t v )t L is the minimal polynomial of a pn-sequence, then the sequence can be generated by a windmill generator. For L = 1, ...127, and ν = 4, 8, 16 such that L ≡ ±3 mod 8 no irreducible polynomials f(t) were found. When L ≡ ±1 mod 8 the number of primitive f(t)’s was found to be approximately twice the expected number.


  1. [1]
    European Broadcasting Union: “Specification of the systems of the MAC/packet family)”, Tech 3258-E (Brussels: EBU technical centre), 1986.Google Scholar
  2. [2]
    A. Lempel, W.L. Eastman, “High speed generation of maximal length sequences”, IEEE Trans. on Comput., Vol. C-20, (1971), pp. 227–229.CrossRefGoogle Scholar
  3. [3]
    A.C. Arvillias, D.G. Maritsas, “Combinational logicfree realisations for high-speed m-sequence generation”, Electronics Letters, Vo1.13, no.17, (1977), pp. 500–502.CrossRefGoogle Scholar
  4. [4]
    F. Surböck, H. Weinrichter, “Interlacing properties of shift-register sequences with generator polynomials irreducible over GF(p)”, IEEE Trans. on Inform. Theory, Vol. IT-24, (1978), pp. 386–389.CrossRefGoogle Scholar
  5. [5]
    B.J.M. Smeets. On Linear Recurring Sequences, PhD dissertation, University of Lund, 1987.Google Scholar
  6. [6]
    R. Lidl, H. Niederreiter, Finite Fields, Encyclopedia of Mathematics and its Applications, Vol. 20, Addison-Wesley, Reading, Mass, 1983.Google Scholar
  7. [7]
    S.D. Cohen, “Windmill polynomials over fields of characteristic two”, preprint.Google Scholar
  8. [8]
    E.R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, New York, 1968.MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • B. J. M. Smeets
    • 1
  • W. G. Chambers
    • 2
  1. 1.Dept of Inform. TheoryUniversity of LundLundSweden
  2. 2.Dept of Eletronic and Electrical EngineeringKing’s College LondonStrand, LondonUK

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