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September 2016 Characterization of Sporadic perfect polynomials over $\mathbb{F}_2$
Luis H. Gallardo, Olivier Rahavandrainy
Funct. Approx. Comment. Math. 55(1): 7-21 (September 2016). DOI: 10.7169/facm/2016.55.1.1

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 $a,b, h \in \mathbb{N}^*$.

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Luis H. Gallardo. Olivier Rahavandrainy. "Characterization of Sporadic perfect polynomials over $\mathbb{F}_2$." Funct. Approx. Comment. Math. 55 (1) 7 - 21, September 2016. https://doi.org/10.7169/facm/2016.55.1.1

Information

Published: September 2016
First available in Project Euclid: 19 September 2016

zbMATH: 06862549
MathSciNet: MR3549009
Digital Object Identifier: 10.7169/facm/2016.55.1.1

Subjects:
Primary: 11T55
Secondary: 11T06

Rights: Copyright © 2016 Adam Mickiewicz University

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Vol.55 • No. 1 • September 2016
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