Journal of Electronic Testing

, Volume 19, Issue 6, pp 645–657 | Cite as

Primitive Polynomials Over GF(2) of Degree up to 660 with Uniformly Distributed Coefficients

  • Janusz Rajski
  • Jerzy Tyszer


New tables of primitive polynomials of degree up to 660 over the Galois field of 2 elements are provided. These polynomials have been obtained for ring generators—a new class of linear feedback shift registers featuring enhanced properties over conventional shift registers. For each degree polynomials with five, seven and nine nonzero coefficients are presented. The coefficients are uniformly separated from each other so that the resulting implementations are highly modular.

linear feedback shift registers primitive polynomials ring generators 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P.H. Bardell, “Primitive Polynomials of Degree 301 Through 500,” J. of Electronic Testing: Theory and Applications, vol. 3, pp. 175-176, 1992.Google Scholar
  2. 2.
    J.T.B. Beard, Jr. and K.I. West, “Some Primitive Polynomials of the Third Kind,” Math. Comp., vol. 28, pp. 1166-1167, 1974.Google Scholar
  3. 3.
    F. Blake, S. Gao, and R. Lambert, “Constructive Problems for Irreducible Polynomials Over Finite Fields,” Lecture Notes in Computer Science, Springer-Verlag, vol. 793, pp. 1-23, 1994.Google Scholar
  4. 4.
    T. Hansen and G.L. Mullen, “Primitive Polynomials Over Finite Fields,” Math. Comp., vol. 59, pp. 639-643, 1992.Google Scholar
  5. 5.
    G. Mrugalski, J. Rajski, and J. Tyszer, “Cellular Automata-Based Test Pattern Generators with Phase Shifters,” IEEE Trans. on Computer Aided Design, vol. 19, pp. 878-893, 2000.Google Scholar
  6. 6.
    G. Mrugalski, J. Rajski, and J. Tyszer, “High Speed Ring Generators and Compactors of Test Data,” in Proc. VLSI Test Symposium, 2003, pp. 57-62.Google Scholar
  7. 7.
    W.W. Peterson and E.J. Weldon, Jr., Error-Correcting Codes, MIT Press, Cambridge, 1972.Google Scholar
  8. 8.
    J. Rajski, J. Tyszer, M. Kassab, N. Mukherjee, R. Thompson, H. Tsai, A. Hertwig, N. Tamarapalli, G. Mrugalski, G. Eide, and J. Qian, “Embedded Deterministic Test for Low Cost Manufacturing Test,” in Proc. Int. Test Conf., 2002, pp. 301-310.Google Scholar
  9. 9.
    W. Stahnke, “Primitive Binary Polynomials,” Math. Comp., vol. 27, pp. 977-980, 1973.Google Scholar
  10. 10.
    E. Sugimoto, “A Short Note on New Indexing Polynomials of Finite Fields,” Inform. and Control, vol. 41, pp. 243-246, 1979.Google Scholar
  11. 11.
    E.J. Watson, “Primitive Polynomials (mod 2),” Math. Comp., vol. 16, pp. 368-369, 1962.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Janusz Rajski
    • 1
  • Jerzy Tyszer
    • 2
  1. 1.Mentor Graphics CorporationWilsonville, ORUSA
  2. 2.PoznańUniversity of TechnologyPoznańPoland

Personalised recommendations