 # Finite Field Tables

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A field is a set of elements with the four operations of arithmetic satisfying the following properties.  associativity: , ,  commutativity: , distributivity: , zero and identity: ,  inverses if .

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One example of a field is the set of numbers {0,1,2,3,4} modulo 5, and similarly any prime number gives a field, GF( ). A Galois field is a finite field with order a prime power ; these are the only finite fields, and can be represented by polynomials with coefficients in GF( ) reduced modulo some polynomial.

In this Demonstration, pick a prime and polynomial, and the corresponding addition and multiplication tables within that finite field will be shown. Squares colored by grayscale represent the fiield elements.

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Contributed by: Ed Pegg Jr (March 2011)
Open content licensed under CC BY-NC-SA

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Ed Pegg Jr

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