Communications Toolbox

Galois Field Computations

A Galois field is an algebraic field that has a finite number of members. Galois fields having 2^m members are used in error-control coding and are denoted GF(2^m). This chapter describes how to work with fields that have 2^m members, where m is an integer between 1 and 16. The sections in this chapter are as follows.

Galois Field Terminology	Definitions of terms as used in this chapter
Representing Elements of Galois Fields	Creating a MATLAB array containing elements of a Galois field
Arithmetic in Galois Fields	Doing arithmetic with arrays of Galois field elements
Logical Operations in Galois Fields	Testing for equality or for nonzero values
Matrix Manipulation in Galois Fields	Working with arrays of Galois field elements
Linear Algebra in Galois Fields	Solving linear equations, inverting arrays, and performing other linear algebraic computations
Signal Processing Operations in Galois Fields	Filtering, convolution, and discrete Fourier transforms
Polynomials over Galois Fields	Representing and performing computations with polynomials
Manipulating Galois Variables	Working with variables that represent Galois field elements
Speed and Nondefault Primitive Polynomials	Accelerating computations involving Galois field elements expressed relative to a nondefault primitive polynomial
Selected Bibliography for Galois Fields	Works containing background information about Galois fields or their use in error-control coding

If you need to use Galois fields having an odd number of elements, see Galois Fields of Odd Characteristic in the online documentation for the Communications Toolbox.

For more details about specific functions that process arrays of Galois field elements, see the online reference entries in the documentation for MATLAB or for the Communications Toolbox. MATLAB functions whose generalization to Galois fields is straightforward to describe do not have reference entries in this manual because the entries would be identical to those in the MATLAB manual.

Selected Bibliography for Equalizers

Galois Field Terminology