# 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[edit]

Over GF(2) the ESP has many interesting 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.

## References[edit]