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:

“It was the custom
For his rage against chaos
To abate on the way to church,
In regulations of his spirit.
How good life is, on the basis of propriety,
To be followed by a platter of capon!”
—Wallace Stevens (1879–1955)