A criterion for primitive polynomials over Galois rings

作者：Zhu, YF^*; Wang, XL

来源：Discrete Mathematics, 2005, 303(1-3): 243-255.

DOI：10.1016/j.disc.2004.12.026

• Galois rings
• finite fields
• primitive polynomials
• linear recurring series

In this paper, we present a link between the representation of a root of a basic irreducible polynomial f(x) 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 f (x) mod p and f (x) mod p(2), respectively. By these results, we can give some fine criteria for primitive polynomials over Galois rings with characteristic 2(n), and characterize trinomial and pentanomial primitive polynomials over Z(2n) Completely.

• 出版日期2005-11-6
• 单位广州大学