Communications Toolbox

Representing Elements of Galois Fields

This section discusses how to represent Galois field elements using this toolbox's exponential format and polynomial format. It also describes a way to list all elements of the Galois field, because some functions use such a list as an input argument. Finally, it discusses the nonuniqueness of representations of Galois field elements.

The elements of GF(p) can be represented using the integers from 0 to p-1.

When m is at least 2, GF(p^m) is called an extension field. Integers alone cannot represent the elements of GF(p^m) in a straightforward way. MATLAB uses two main conventions for representing elements of GF(p^m): the exponential format and the polynomial format.

Note    Both the exponential format and the polynomial format are relative to your choice of a particular primitive element A of GF(pm).

Galois Field Terminology

Exponential Format