New primitive $t$-nomials $(t = 3,5)$ over $GF(2)$ whose degree is a Mersenne exponent
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- by Toshihiro Kumada, Hannes Leeb, Yoshiharu Kurita and Makoto Matsumoto PDF
- Math. Comp. 69 (2000), 811-814 Request permission
Corrigendum: Math. Comp. 71 (2002), 1337-1338.
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.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1665959