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:

    “Even upon such a basis hast thou built
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    —George Gordon Noel Byron (1788–1824)