Corrigenda to βNew primitive $t$-nomials $(t=3,5)$ over $GF(2)$ whose degree is a Mersenne exponent,β and some new primitive pentanomials
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- by Toshihiro Kumada, Hannes Leeb, Yoshiharu Kurita and Makoto Matsumoto PDF
- Math. Comp. 71 (2002), 1337-1338 Request permission
Abstract:
We report an error in our previous paper [New primitive t-nomials $(t=3,5)$ over $GF(2)$ whose degree is a Mersenne exponent, Math. Comp. 69 (2000), no. 230, 811β814], where we announced that we listed all the primitive trinomials over $GF(2)$ of degree 859433, but there is a bug in the sieve. We missed the primitive trinomial $X^{859433}+X^{170340}+1$ and its reciprocal, as pointed out by Richard Brent et al. We also report some new primitive pentanomials.References
- R. P. Brent, S. Larvala and P. Zimmermann, A fast algorithm for testing irreducibility of trinomials mod $2$ (preliminary report), Report PRG TR-13-00, 30 December 2000. Available from http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pub/pub199.html.
- Toshihiro Kumada, Hannes Leeb, Yoshiharu Kurita, and Makoto Matsumoto, New primitive $t$-nomials $(t=3,5)$ over $\rm GF(2)$ whose degree is a Mersenne exponent, Math. Comp. 69 (2000), no.Β 230, 811β814. MR 1665959, DOI 10.1090/S0025-5718-99-01168-0
Additional Information
- Toshihiro Kumada
- Affiliation: Daiwa Institute of Research Ltd. 15-6 Fuyuki, Koto-ku, Tokyo 135-8460, Japan
- Email: t.kumada@dir.co.jp
- Hannes Leeb
- Affiliation: Institute of Statistics, University of Vienna, Universitaetsstr. 5, 1010 Vienna, Austria
- Email: Hannes.Leeb@univie.ac.at
- Yoshiharu Kurita
- Affiliation: Nippon Electric Control Equipment Industries Association, 2-1-17 Hamamatsu-cho, Minato-ku, Tokyo 105-0013 Japan
- Email: ykurit@attglobal.net
- Makoto Matsumoto
- Affiliation: Division of Mathematics, Integrated Human Studies, Kyoto University, Kyoto 606-8501 Japan
- Email: matumoto@math.h.kyoto-u.ac.jp
- Received by editor(s): May 10, 2001
- Published electronically: April 1, 2002
- © Copyright 2002 American Mathematical Society
- Journal: Math. Comp. 71 (2002), 1337-1338
- MSC (2000): Primary 11-04, 11T06, 12-04, 12E05
- DOI: https://doi.org/10.1090/S0025-5718-02-01487-4
- MathSciNet review: 1898761