New primitive 𝑡-nomials (𝑡=3,5) over 𝐺𝐹(2) whose degree is a Mersenne exponent

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

doi:10.1090/S0025-5718-99-01168-0

New primitive $t$-nomials $(t = 3,5)$ over $GF(2)$ whose degree is a Mersenne exponent
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by Toshihiro Kumada, Hannes Leeb, Yoshiharu Kurita and Makoto Matsumoto PDF

Math. Comp. 69 (2000), 811-814 Request permission

Corrigendum: Math. Comp. 71 (2002), 1337-1338.

Abstract:

All primitive trinomials over $GF(2)$ with degree 859433 (which is the 33rd Mersenne exponent) are presented. They are $X^{859433}+X^{288477}+1$ and its reciprocal. Also two examples of primitive pentanomials over $GF(2)$ with degree 86243 (which is the 28th Mersenne exponent) are presented. The sieve used is briefly described.

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