# Polynomial Form of Binary Cyclotomic Polynomials

## TL;DR

This paper derives a closed form polynomial expression for binary cyclotomic polynomials, providing a new explicit formula that enhances understanding and computation of these mathematical objects.

## Contribution

It introduces a novel closed form polynomial expression for binary cyclotomic polynomials, improving upon previous representations.

## Key findings

- Provides a new explicit polynomial formula for binary cyclotomic polynomials.
- Contrasts the new expression with previous works by Lam and Leung (1996) and Lenstra (1979).
- Enhances computational and theoretical understanding of binary cyclotomic polynomials.

## Abstract

This paper presents a closed form polynomial expression for the binary cyclotomic polynomial. We contrast this against expressions for binary cyclotomic polynomials in (Lam and Leung 1996) and (Lenstra 1979).