GF

GF[p, d]
gives the Galois field that is a degree d extension of the prime field of p elements.

GF[q]
gives the Galois field with q elements, for q a prime power.

GF[p, ilist]
represents the Galois field with prime characteristic p and an irreducible polynomial whose coefficient list is given by ilist.

GF[p, ilist][elist]
represents an element of the Galois field GF[p, ilist] whose polynomial representation has coefficient list elist.

To use GF, you first need to load the Finite Fields Package using Needs["FiniteFields`"].