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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

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
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.


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DOI: http://dx.doi.org/10.1090/S0025-5718-1991-1068813-6
PII: S 0025-5718(1991)1068813-6
Article copyright: © Copyright 1991 American Mathematical Society