Primitive polynomial (field theory)
Minimal polynomial of a primitive element in a finite field / From Wikipedia, the free encyclopedia
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For polynomials such that the greatest common divisor of the coefficients is 1, see Primitive polynomial (ring theory).
In finite field theory, a branch of mathematics, a primitive polynomial is the minimal polynomial of a primitive element of the finite field GF(pm). This means that a polynomial F(X) of degree m with coefficients in GF(p) = Z/pZ is a primitive polynomial if it is monic and has a root α in GF(pm) such that is the entire field GF(pm). This implies that α is a primitive (pm − 1)-root of unity in GF(pm).
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