Equally spaced polynomial - Definition

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:

<math>

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

or

<math>

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

Properties

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

• The Hamming weight of the ESP is m + 1

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