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Galois Field Computations

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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

• Representing Elements of Galois Fields

• Arithmetic in Galois Fields

• Logical Operations in Galois Fields

• Matrix Manipulation in Galois Fields

• Linear Algebra in Galois Fields

• Signal Processing Operations in Galois Fields

• Polynomials over Galois Fields

• Manipulating Galois Variables

• Speed and Nondefault Primitive Polynomials

• Selected Bibliography for Galois Fields

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

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

Selected Bibliography for Equalizers

Galois Field Terminology

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