Functiones et Approximatio Commentarii Mathematici

Characterization of Sporadic perfect polynomials over $\mathbb{F}_2$

Luis H. Gallardo and Olivier Rahavandrainy

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Abstract

We complete, in this paper, the characterization of all known even perfect polynomials over the prime field $\mathbb{F}_2$. In particular, we prove that the last two of the eleven known ``sporadic'' perfect polynomials over $\mathbb{F}_2$ are the unique of them of the form $x^a(x+1)^b M^{2h} \sigma(M^{2h})$, where $M$ is a Mersenne prime and $a,b, h \in \mathbb{N}^*$.

Article information

Source
Funct. Approx. Comment. Math., Volume 55, Number 1 (2016), 7-21.

Dates
First available in Project Euclid: 19 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.facm/1474301226

Digital Object Identifier
doi:10.7169/facm/2016.55.1.1

Mathematical Reviews number (MathSciNet)
MR3549009

Zentralblatt MATH identifier
06862549

Subjects
Primary: 11T55: Arithmetic theory of polynomial rings over finite fields
Secondary: 11T06: Polynomials

Keywords
sum of divisors polynomials finite fields characteristic $2$

Citation

Gallardo, Luis H.; Rahavandrainy, Olivier. Characterization of Sporadic perfect polynomials over $\mathbb{F}_2$. Funct. Approx. Comment. Math. 55 (2016), no. 1, 7--21. doi:10.7169/facm/2016.55.1.1. https://projecteuclid.org/euclid.facm/1474301226


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