Even perfect polynomials over $F_2$ with four prime factors

Luis H. Gallardo; Olivier Rahavandrainy

Even perfect polynomials over $F_2$ with four prime factors

Number Theory 2007-12-18 v1

Authors: Luis H. Gallardo , Olivier Rahavandrainy

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 $\F_2$ .

Keywords

perfect polynomials binary field even polynomials prime factors divisors $\F_2[x]$

Cite

@article{arxiv.0712.2602,
  title  = {Even perfect polynomials over $F_2$ with four prime factors},
  author = {Luis H. Gallardo and Olivier Rahavandrainy},
  journal= {arXiv preprint arXiv:0712.2602},
  year   = {2007}
}

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19 pages (in 12 pt)

Even perfect polynomials over $F_2$ with four prime factors

Abstract

Keywords

Cite

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