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Primitive $ t$-nomials $ (t=3,5)$ over $ {\rm GF}(2)$ whose degree is a Mersenne exponent $ \le 44497$


Authors: Yoshiharu Kurita and Makoto Matsumoto
Journal: Math. Comp. 56 (1991), 817-821
MSC: Primary 11T06; Secondary 11A41
DOI: https://doi.org/10.1090/S0025-5718-1991-1068813-6
MathSciNet review: 1068813
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Abstract: All of the primitive trinomials over $ GF(2)$ with degree p given by one of the Mersenne exponents 19937, 21701, 23209, and 44497 are presented. Also, one example of a primitive pentanomial over $ GF(2)$ is presented for each degree up to 44497 that is a Mersenne exponent. The sieve used is briefly described. A problem is posed which conjectures the number of primitive pentanomials of degree p.


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

  • [1] E. R. Berlekamp, Algebraic coding theory, McGraw-Hill, New York, 1968. MR 0238597 (38:6873)
  • [2] R. Lidl and H. Niederreiter, Introduction to finite fields and their applications, Cambridge Univ. Press, Cambridge, 1986. MR 860948 (88c:11073)
  • [3] E. R. Rodemich and H. Rumsey, Jr., Primitive trinomials of high degree, Math. Comp. 22 (1968), 863-865. MR 0238813 (39:177)
  • [4] W. Stahnke, Primitive binary polynomials, Math. Comp. 27 (1973), 977-980. MR 0327722 (48:6064)
  • [5] E. J. Watson, Primitive polynomials $ \pmod 2$, Math. Comp. 16 (1962), 368-369. MR 0148256 (26:5764)
  • [6] N. Zierler and J. Brillhart, On primitive trinomials $ \pmod 2$, Inform. and Control 13 (1968), 541-554; II, 14 (1969), 566-569.
  • [7] N. Zierler, Primitive trinomials whose degree is a Mersenne exponent, Inform. and Control 15 (1969), 67-69. MR 0244205 (39:5522)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1991-1068813-6
Article copyright: © Copyright 1991 American Mathematical Society

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