Primitive Polynomials Over GF(2) of Degree up to 660 with Uniformly Distributed Coefficients
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
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.
- P.H. Bardell, “Primitive Polynomials of Degree 301 Through 500,” J. of Electronic Testing: Theory and Applications, vol. 3, pp. 175-176, 1992.
- J.T.B. Beard, Jr. and K.I. West, “Some Primitive Polynomials of the Third Kind,” Math. Comp., vol. 28, pp. 1166-1167, 1974.
- 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.
- T. Hansen and G.L. Mullen, “Primitive Polynomials Over Finite Fields,” Math. Comp., vol. 59, pp. 639-643, 1992.
- 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.
- 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.
- W.W. Peterson and E.J. Weldon, Jr., Error-Correcting Codes, MIT Press, Cambridge, 1972.
- 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.
- W. Stahnke, “Primitive Binary Polynomials,” Math. Comp., vol. 27, pp. 977-980, 1973.
- E. Sugimoto, “A Short Note on New Indexing Polynomials of Finite Fields,” Inform. and Control, vol. 41, pp. 243-246, 1979.
- E.J. Watson, “Primitive Polynomials (mod 2),” Math. Comp., vol. 16, pp. 368-369, 1962.
- Primitive Polynomials Over GF(2) of Degree up to 660 with Uniformly Distributed Coefficients
Journal of Electronic Testing
Volume 19, Issue 6 , pp 645-657
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- linear feedback shift registers
- primitive polynomials
- ring generators
- Industry Sectors