Communications Toolbox

Galois Field Computations

A Galois field is an algebraic field that has a finite number of elements. The number of elements is always of the form p^m, where p is a prime number and m is a positive integer. Galois fields are used in error-control coding.

Galois Field Features of the Toolbox

The Communications Toolbox provides functions for manipulating elements of Galois fields, working with polynomials over Galois fields, and performing other tasks related to Galois fields. This section discusses these topics:

• Galois Field Terminology
• Representing Elements of Galois Fields
• Default Primitive Polynomials
• Converting and Simplifying Element Formats
• Arithmetic in Galois Fields
• Polynomials over Prime Fields

For background information about Galois fields or their use in error-control coding, see the works listed in Selected Bibliography for Galois Fields.

Selected Bibliography for Special Filters

Galois Field Terminology