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

Author(s): Toshihiro Kumada; Hannes Leeb; Yoshiharu Kurita; Makoto Matsumoto.
Journal: Math. Comp. 71 (2002), 1337-1338.
MSC (2000): Primary 11-04, 11T06, 12-04, 12E05
Posted: April 1, 2002
Original article: Math. Comp. 69 (2000), 811-814.
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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.

References:

1.
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.

2.
T. Kumada, H. Leeb, Y. Kurita and M. Matsumoto, New primitive t-nomials $(t=3,5)$ over $GF(2)$ whose degree is a Mersenne exponent, Math. Comp. 69 (2000), no. 230, 811-814. MR 2000i:11183

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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, \mbox{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: 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
Posted: April 1, 2002
Copyright of article: Copyright 2002, American Mathematical Society

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