Communications Toolbox

Appendix: Galois Fields of Odd Characteristic

A Galois field is an algebraic field that has a finite number of members. The number of elements is always of the form p^m, where p is a prime number and m is a positive integer. This section describes how to work with fields that have p^m, where p is an odd prime number. To work with Galois fields having an even number of elements, see Galois Field Computations. The topics covered here are as follows.

Galois Field Terminology	Definitions of some terms related to Galois fields
Representing Elements of Galois Fields	How to represent Galois field elements using exponential and polynomial formats
Default Primitive Polynomials	How to determine the toolbox's default primitive polynomial for a Galois field
Converting and Simplifying Element Formats	How to convert between the exponential and polynomial formats, and how to simplify a given representation
Arithmetic in Galois Fields	How to add, subtract, multiply, and divide elements of Galois fields
Polynomials over Prime Fields	How to manipulate and find roots of polynomials over a prime Galois field; how to find primitive polynomials
Other Galois Field Functions	List of other functions that are related to Galois fields
Selected Bibliography for Galois Fields	Reference works that offer more information about Galois fields

Selected Bibliography for Galois Fields Galois Field Terminology