Corrigenda to โNew primitive ๐ก-nomials (๐ก=3,5) over ๐บ๐น(2) whose degree is a Mersenne exponent,โ and some new primitive pentanomials
Toshihiro Kumada, Hannes Leeb, Yoshiharu Kurita, Makoto Matsumoto ยท Mathematics of Computation ยท 2002
We report an error in our previous paper [ New primitive t-nomials ( t = 3 , 5 ) (t=3,5) over G F ( 2 ) GF(2) whose degree is a Mersenne exponent , Math. Comp. 69 (2000), no. 230, 811โ814], where we announced that we listed all the primitive trinomials over G F ( 2 ) GF(2) of degree 859433, but there is a bug in the sieve. We missed the primitive trinomial X 859433 + X 170340 + 1 X^{859433}+X^{170340}+1 and its reciprocal, as pointed out by Richard Brent et al. We also report some new primitive pentanomials.