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.

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