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:

“Reason looks at necessity as the basis of the world; reason is able to turn chance in your favor and use it. Only by having reason remain strong and unshakable can we be called a god of the earth.”
—Johann Wolfgang Von Goethe (1749–1832)