A Galois field is a field with finite number of elements. Galois fields take one of two forms:

• Z_p - The integers modulo some prime p.
• F_p^n - The polynomials with coefficients modulo some prime p with operations modulo some irreducible degree n polynomial r(x).

In either case, the Galois field with q=pⁿ elements is commonly denoted GFq or F_q.