Equally spaced polynomial

From Wikipedia, the free encyclopedia

An equally spaced polynomial (ESP) is a polynomial used in finite fields, specifically GF(2) (binary).

An s-ESP of degree sm can be written as:

ESP(x) = \sum_{i=0}^{m} x^{si} for i = 0, 1, \ldots, m

or

ESP(x) = x^{sm} + x^{s(m-1)} + \cdots + x^s + 1

[edit] Properties

Over GF(2) the ESP has many interest properties, including:

A 1-ESP is known as an all one polynomial and has additional properties including the above.

Retrieved from "http://en.wikipedia.org../../../e/q/u/Equally_spaced_polynomial.html"