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
The set of elements of GF(pm) can then be represented as:
using Zech's logarithms.
Read more about Polynomial Basis: Addition, Multiplication, Squaring, Inversion, Usage
Famous quotes containing the word basis:
“Knighterrantry is a most chuckleheaded trade, and it is tedious hard work, too, but I begin to see that there is money in it, after all, if you have luck. Not that I would ever engage in it, as a business, for I wouldnt. No sound and legitimate business can be established on a basis of speculation. A successful whirl in the knighterrantry linenow what is it when you blow away the nonsense and come down to the cold facts? Its just a corner in pork, thats all.”
—Mark Twain [Samuel Langhorne Clemens] (18351910)