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Chapter 22 Finite Fields

Finite fields appear in many applications of algebra, including coding theory and cryptography. We already know one finite field, Zp, where p is prime. In this chapter we will show that a unique finite field of order pn exists for every prime p, where n is a positive integer. Finite fields are also called Galois fields in honor of Γ‰variste Galois, who was one of the first mathematicians to investigate them.