Contents

Index

• Getting Started

• User's Guide

• Signal Sources

• Performance Evaluation

• Error Rate Test Console

• BERTool: A Bit Error Rate Analysis GUI

• Source Coding

• Error Detection and Correction

• Interleaving

• Special Filters

• Galois Field Computations

• EyeScope: An Eye Diagram Analysis Tool

• Working with Embedded MATLAB Subset in Communications Toolbox

• Galois Fields of Odd Characteristic

Galois Field Terminology

• Representing Elements of Galois Fields

Section Overview

Exponential Format

Polynomial Format

List of All Elements of a Galois Field

Nonuniqueness of Representations

Default Primitive Polynomials

• Converting and Simplifying Element Formats

Converting to Simplest Polynomial Format

Example: Generating a List of Galois Field Elements

Converting to Simplest Exponential Format

• Arithmetic in Galois Fields

Section Overview

Arithmetic in Prime Fields

Arithmetic in Extension Fields

• Polynomials over Prime Fields

Section Overview

Cosmetic Changes of Polynomials

Polynomial Arithmetic

Characterization of Polynomials

Roots of Polynomials

Other Galois Field Functions

Selected Bibliography for Galois Fields

• Analytical Expressions Used in berawgn, bercoding, berfading, and BERTool

• Release Notes

Learn more about Communications Toolbox

Galois Fields of Odd Characteristic

A Galois field is an algebraic field having p^m elements, where p is prime and m is a positive integer. This chapter describes how to work with Galois fields in which p is odd. To work with Galois fields having an even number of elements, see Galois Field Computations. The sections in this chapter are as follows.

Supported Functions

Supported Functions

Galois Field Terminology

Galois Field Terminology

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