Fields of Beer February 21, 2006

A field is a set of elements that is closed under, and satisfies the axioms of, associativity, commutativity, distributivity, identity and inverse, for addition and multiplication. The number of elements in a field Zp is p, and p is always prime (or a power of a prime).

A field with a finite number of elements is called a Galois Field. As an aside to this aside, in looking at error correcting codes, a binary code (alphabet {0, 1}) with codewords of length n has all its codes in the field GF(2n). GF(2n) is a vector space of n-tuples over GF(2).

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