English

Admissible family for binary perfect polynomials

Number Theory 2022-02-17 v1

Abstract

The paper is about an arithmetic problem in \F2[x]\F_2[x]. We give \emph{admissible} (necessary) conditions satisfied by a set of odd prime divisors of perfect polynomials over \F2\F_2. This allows us to prove a new characterization of \emph{all} known perfect polynomials, and to open a way of finding more of them (if they exist).

Keywords

Cite

@article{arxiv.2202.08126,
  title  = {Admissible family for binary perfect polynomials},
  author = {Luis H. Gallardo and Olivier Rahavandrainy},
  journal= {arXiv preprint arXiv:2202.08126},
  year   = {2022}
}

Comments

12 pages

R2 v1 2026-06-24T09:41:07.694Z