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

 

Corrigenda to ``New primitive $t$-nomials $(t=3,5)$ over $GF(2)$ whose degree is a Mersenne exponent,'' and some new primitive pentanomials


Authors: Toshihiro Kumada, Hannes Leeb, Yoshiharu Kurita and Makoto Matsumoto
Journal: Math. Comp. 71 (2002), 1337-1338
MSC (2000): Primary 11-04, 11T06, 12-04, 12E05
Published electronically: April 1, 2002
Original Article: Math. Comp. 69 (2000), 811-814.
MathSciNet review: 1898761
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Abstract: We report an error in our previous paper [#!K1!#], 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.


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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

DOI: http://dx.doi.org/10.1090/S0025-5718-02-01487-4
PII: S 0025-5718(02)01487-4
Keywords: Irreducible polynomials, primitive polynomials, finite field, Mersenne exponent
Received by editor(s): May 10, 2001
Published electronically: April 1, 2002
Article copyright: © Copyright 2002 American Mathematical Society