Equally spaced polynomial

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:

for

or

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.