A criterion for primitive polynomials over Galois rings Original Research Article

In this paper, we present a link between the representation of a root of a basic irreducible polynomial image over a Galois ring and its order, and derive algebraic discriminants for primitive polynomials and sub-primitive polynomials, respectively. The principal parts of these discriminants are determined by the coefficients of image and image, respectively. By these results, we can give some fine criteria for primitive polynomials over Galois rings with characteristic image, and characterize trinomial and pentanomial primitive polynomials over image completely.