Corrigenda to “New primitive 𝑡-nomials (𝑡=3,5) over 𝐺𝐹(2) whose degree is a Mersenne exponent,” and some new primitive pentanomials

Kumada, Toshihiro; Leeb, Hannes; Kurita, Yoshiharu; Matsumoto, Makoto

doi:10.1090/S0025-5718-02-01487-4

Corrigenda to “New primitive $t$-nomials $(t=3,5)$ over $GF(2)$ whose degree is a Mersenne exponent,” 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, 811–814], 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. 230, 811–814. MR 1665959, DOI 10.1090/S0025-5718-99-01168-0