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based on an earlier version of the Wolfram Language.
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GF[p, d]
gives the Galois field that is a degree d extension of the prime field of p elements.
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.