Dear Clinton,

all irreducible polynomials of degree n over GF(2) can be obtained by
factoring x^(2^n)+x, and keeping only factors of degree n:

sage: P.<x> = GF(2)[]
sage: factor(x^(2^5)+x)
x * (x + 1) * (x^5 + x^2 + 1) * (x^5 + x^3 + 1) * (x^5 + x^3 + x^2 + x + 1) * 
(x^5 + x^4 + x^2 + x + 1) * (x^5 + x^4 + x^3 + x + 1) * (x^5 + x^4 + x^3 + x^2 
+ 1)

Paul Zimmermann

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