Communications Toolbox

Galois Field Terminology

Throughout this section, p is an odd prime number and m is a positive integer.

Also, this document uses a few terms that are not used consistently in the literature. The definitions adopted here appear in van Lint [4].

• A primitive element of GF(p^m) is a cyclic generator of the group of nonzero elements of GF(p^m). This means that every nonzero element of the field can be expressed as the primitive element raised to some integer power. Primitive elements are called A throughout this section.
• A primitive polynomial for GF(p^m) is the minimal polynomial of some primitive element of GF(p^m). As a consequence, it has degree m and is irreducible.

Representing Elements of Galois Fields