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## Appendix C Galois Fields

Galois fields and their properties are critical to the development and implementation of error-correction codes, as discussed in Chapter 16

### C.1 Finite Fields

The operations of modulo-5 addition and multiplication are defined in Table C.1. Modulo-5 addition over the set of integers {0, 1, 2, 3, 4} is an example of a commutative group because it exhibits the following properties:

The set of integers {0, 1, 2, 3, 4} is closed under the operation of modulo-5 addition; that is, the addition of any two elements produces a result that is also an element of the set {0, 1, 2, 3, 4}.

Modulo-5 addition is commutative: a + b =

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