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

Toshihiro Kumada; Hannes Leeb; Yoshiharu Kurita; Makoto Matsumoto

doi:https://doi.org/10.1090/s0025-5718-99-01168-0

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

Toshihiro Kumada, Hannes Leeb, Yoshiharu Kurita, Makoto Matsumoto · Mathematics of Computation · 1999

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

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