Polynomial Basis

In mathematics, the polynomial basis is a basis for finite extensions of finite fields.

Let α ∈ GF(pm) be the root of a primitive polynomial of degree m over GF(p). The polynomial basis of GF(pm) is then

$\{ 1, \alpha, \ldots, \alpha^{m-1}\}$

The set of elements of GF(pm) can then be represented as:

$\{ 0, 1, \alpha, \alpha^2, \ldots, \alpha^{p^{m}-2} \}$

using Zech's logarithms.

Read more about Polynomial Basis: Addition, Multiplication, Squaring, Inversion, Usage

Famous quotes containing the word basis:

“The basis of world peace is the teaching which runs through almost all the great religions of the world. “Love thy neighbor as thyself.” Christ, some of the other great Jewish teachers, Buddha, all preached it. Their followers forgot it. What is the trouble between capital and labor, what is the trouble in many of our communities, but rather a universal forgetting that this teaching is one of our first obligations.”
—Eleanor Roosevelt (1884–1962)