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Primitive binary polynomials


Author: Wayne Stahnke
Journal: Math. Comp. 27 (1973), 977-980
MSC: Primary 12C05; Secondary 12-04
DOI: https://doi.org/10.1090/S0025-5718-1973-0327722-7
MathSciNet review: 0327722
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Abstract | References | Similar Articles | Additional Information

Abstract: One primitive polynomial modulo two is listed for each degree n through $ n = 168$. Each polynomial has the minimum number of terms possible for its degree. The method used to generate the list is described.


References [Enhancements On Off] (What's this?)

  • [1] P. H. R. Scholefield, "Shift registers generating maximum-length sequences," Electronic Technology, v. 37, 1960, pp. 389-394.
  • [2] S. W. Golomb, Shift Register Sequences, Holden-Day, San Francisco, Calif., 1967. MR 39 #3906. MR 0242575 (39:3906)
  • [3] E. I. Watson, "Primitive polynomials $ ({\operatorname{Mod}}\;2)$," Math. Comp., v. 16, 1962, pp. 368-369. MR 26 #5764. MR 0148256 (26:5764)
  • [4] E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, New York, 1968. MR 38 #6873. MR 0238597 (38:6873)
  • [5] N. Zierler & J. Brillhart, "On primitive trinomials $ ({\operatorname{Mod}}\;2)$," Information Control, v. 13, 1968, pp. 541-554; II, v. 14, 1969, pp. 566-569. MR 38 #5750; MR 39 #5521.
  • [6] R. W. Marsh, Table of Irreducible Polynomials Over $ GF(2)$ Through Degree 19, Office of Technical Services, Department of Commerce, Washington, D. C., October 24, 1957.
  • [7] H. Riesel, En Bok om Primtal [A Book on Prime Numbers], Studentlitteratur, Lund, 1968. (Swedish) MR 42 #4507. MR 0269612 (42:4507)
  • [8] J. Brillhart, "Some miscellaneous factorizations," Math. Comp., v. 17, 1963, pp. 447-450.
  • [9] J. Brillhart & J. L. Selfridge, "Some factorizations of $ {2^n} \pm 1$ and related results," Math. Comp., v. 21, 1967, pp. 87-96. MR 37 #131. MR 0224532 (37:131)
  • [10] K. R. Isemonger, "Complete factorization of $ {2^{159}} - 1$," Math. Comp., v. 15, 1961, pp. 295-296. MR 23 #A1577. MR 0124263 (23:A1577)
  • [11] K. R. Isemonger, "Some additional factorizations of $ {2^n} \pm 1$," Math. Comp., v. 19, 1965, pp. 145-146. MR 30 #1081. MR 0170846 (30:1081)
  • [12] M. Kraitchik, Introduction à la Théorie des Nombres, Gauthier-Villars, Paris, 1952. MR 14, 535. MR 0051845 (14:535a)
  • [13] M. Kraitchik, "On the factorization of $ {2^n} \pm 1$," Scripta Math., v. 18, 1952, pp. 39-52. MR 14, 121. MR 0049113 (14:121e)
  • [14] R. M. Robinson, "Some factorizations of numbers of the form $ {2^n} \pm 1$," MTAC, v. 11, 1957, pp. 265-268. MR 20 #832. MR 0094313 (20:832)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1973-0327722-7
Keywords: Primitive polynomials, finite field, Mersenne numbers, shift-register sequences
Article copyright: © Copyright 1973 American Mathematical Society

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