Odd perfect polynomials over ${𝔽}_2$

Gallardo, Luis H., and Rahavandrainy, Olivier. "Odd perfect polynomials over ${\mathbb{F}_2}$." Journal de Théorie des Nombres de Bordeaux 19.1 (2007): 165-174. <http://eudml.org/doc/249980>.

@article{Gallardo2007,
abstract = {A perfect polynomial over $\mathbb\{F\}_2$ is a polynomial $A \in \mathbb\{F\}_2[x]$ that equals the sum of all its divisors. If $\gcd (A,x^2+x)=1$ then we say that $A$ is odd. In this paper we show the non-existence of odd perfect polynomials with either three prime divisors or with at most nine prime divisors provided that all exponents are equal to $2.$},
affiliation = {Université de Brest 6, Avenue Le Gorgeu, C.S. 93837 29238 Brest cedex 3, France; Université de Brest 6, Avenue Le Gorgeu, C.S. 93837 29238 Brest cedex 3, France},
author = {Gallardo, Luis H., Rahavandrainy, Olivier},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {finite field; polynomial},
language = {eng},
number = {1},
pages = {165-174},
publisher = {Université Bordeaux 1},
title = {Odd perfect polynomials over $\{\mathbb\{F\}_2\}$},
url = {http://eudml.org/doc/249980},
volume = {19},
year = {2007},
}

TY - JOUR
AU - Gallardo, Luis H.
AU - Rahavandrainy, Olivier
TI - Odd perfect polynomials over ${\mathbb{F}_2}$
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2007
PB - Université Bordeaux 1
VL - 19
IS - 1
SP - 165
EP - 174
AB - A perfect polynomial over $\mathbb{F}_2$ is a polynomial $A \in \mathbb{F}_2[x]$ that equals the sum of all its divisors. If $\gcd (A,x^2+x)=1$ then we say that $A$ is odd. In this paper we show the non-existence of odd perfect polynomials with either three prime divisors or with at most nine prime divisors provided that all exponents are equal to $2.$
LA - eng
KW - finite field; polynomial
UR - http://eudml.org/doc/249980
ER -