A finite field is a field with only finitely many elements.
Some key facts about finite fields include:
- The characteristic of a finite field must be a prime number.
- The size of a finite field must be a prime power. In fact, it must be a power of the prime number that is the characteristic of the field.
- For any prime power, there is a unique (up to isomorphism) finite field whose size equals that prime power.
Combining the above key facts, we denote, for any prime power , the unique finite field of size by the symbols or . (Note that GF stands for Galois field in recognition of Galois's pioneering work in field theory).
|Field size||Underlying prime (field characteristic)||, i.e, the number such that||Field|