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New primitive $t$-nomials $(t=3,5)$ over $GF(2)$
whose degree is a Mersenne exponent


Authors: Toshihiro Kumada, Hannes Leeb, Yoshiharu Kurita and Makoto Matsumoto
Journal: Math. Comp. 69 (2000), 811-814
MSC (1991): Primary 11-04, 11T06, 12-04, 12E05
DOI: https://doi.org/10.1090/S0025-5718-99-01168-0
Published electronically: August 18, 1999
Corrigendum: Math. Comp 71 (2002), 1337-1338
MathSciNet review: 1665959
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Abstract | References | Similar Articles | Additional Information

Abstract: All primitive trinomials over $GF(2)$ with degree 859433 (which is the 33rd Mersenne exponent) are presented. They are $X^{859433}+X^{288477}+1$ and its reciprocal. Also two examples of primitive pentanomials over $GF(2)$ with degree 86243 (which is the 28th Mersenne exponent) are presented. The sieve used is briefly described.


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Additional Information

Toshihiro Kumada
Affiliation: Department of Mathematics, Keio University, Yokohama, Japan
Email: kumada@math.keio.ac.jp

Hannes Leeb
Affiliation: Department of Statistics, OR and Computer Methods, University of Vienna, Austria
Email: leeb@smc.univie.ac.at

Yoshiharu Kurita
Affiliation: Hungarian Productivity Center, Budapest, Hungary
Email: ykurit@ibm.net

Makoto Matsumoto
Affiliation: Department of Mathematics, Keio University, Yokohama, Japan
Email: matumoto@math.keio.ac.jp

DOI: https://doi.org/10.1090/S0025-5718-99-01168-0
Keywords: Irreducible polynomials, primitive polynomials, finite field, Mersenne exponent
Received by editor(s): May 19, 1998
Published electronically: August 18, 1999
Additional Notes: This research was supported by the Austrian Science Foundation (FWF), project no. P11143-MAT
Article copyright: © Copyright 2000 American Mathematical Society

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