Primitive Polynomials over Finite Fields of Characteristic Two

摘要

Let F_q be a finite field of characteristic two. We prove that for any given element a ∈F_q , there exists a primitive polynomial f(x)=x~n - σ_1x~(n-1) + …+(-1)~nσ_n of degree n over F_q with the m-th (0 < m < n) coefficient σ_m =a when n ≥ 7, n is odd