Galois fields

In mathematics a Galois field is a field having a finite number of elements.

Galois fields are one of two types:

• The integers modulo a prime number p, represented by Z_p
• The polynomials with coefficients modulo a prime number p having operations modulo with an irreducible n-degree polynomial r(x), represented by F_p^n

A Galois field with q=p^n elements is typically denoted by GF_q or F_q.