Remote Access Mathematics of Computation
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 11-04, 11T06, 12-04, 12E05

Retrieve articles in all journals with MSC (2000): 11-04, 11T06, 12-04, 12E05

Additional Information

Toshihiro Kumada
Affiliation: Daiwa Institute of Research Ltd. 15-6 Fuyuki, Koto-ku, Tokyo 135-8460, Japan

Hannes Leeb
Affiliation: Institute of Statistics, University of Vienna, Universitaetsstr. 5, 1010 Vienna, Austria

Yoshiharu Kurita
Affiliation: Nippon Electric Control Equipment Industries Association, 2-1-17 Hamamatsu-cho, Minato-ku, Tokyo 105-0013 Japan

Makoto Matsumoto
Affiliation: Division of Mathematics, Integrated Human Studies, Kyoto University, Kyoto 606-8501 Japan

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