# Even perfect polynomials over $F_2$ with four prime factors

- Authors
- Type
- Preprint
- Publication Date
- Dec 16, 2007
- Submission Date
- Dec 16, 2007
- Source
- arXiv
- License
- Unknown
- External links

## Abstract

A perfect polynomial over the binary field $\F_2$ is a polynomial $A \in \F_2[x]$ that equals the sum of all its divisors. If $\gcd(A,x^2-x) \neq 1$ then we call $A$ even. The list of all even perfect polynomials over $\F_2$ with at most 3 prime factors in known. The object of this paper is to give the list of all even perfect polynomials over $\F_2$ with four prime factors. These are all the known perfect polynomials with four prime factors over $\F_2$.