Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Electronic Testing Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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. 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. 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. T. Hansen and G.L. Mullen, “Primitive Polynomials Over Finite Fields,” Math. Comp., vol. 59, pp. 639-643, 1992.

    Google Scholar 

  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. 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.

  7. W.W. Peterson and E.J. Weldon, Jr., Error-Correcting Codes, MIT Press, Cambridge, 1972.

    Google Scholar 

  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.

  9. W. Stahnke, “Primitive Binary Polynomials,” Math. Comp., vol. 27, pp. 977-980, 1973.

    Google Scholar 

  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. E.J. Watson, “Primitive Polynomials (mod 2),” Math. Comp., vol. 16, pp. 368-369, 1962.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mentor Graphics Corporation, 8005 S.W. Boeckman Road, Wilsonville, OR, 97070, USA

    Janusz Rajski

  2. Poznań, University of Technology, ul. Piotrowo 3a, 60-965, Poznań, Poland

    Jerzy Tyszer

Authors
  1. Janusz Rajski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jerzy Tyszer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rajski, J., Tyszer, J. Primitive Polynomials Over GF(2) of Degree up to 660 with Uniformly Distributed Coefficients. Journal of Electronic Testing 19, 645–657 (2003). https://doi.org/10.1023/A:1027422805851

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1027422805851

Search

Navigation