Characterization of Sporadic perfect polynomials over $\mathbb{F}_2$
Luis H. Gallardo, Olivier Rahavandrainy · Functiones et Approximatio Commentarii Mathematici · 2016
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 $a,b, h \in \mathbb{N}^*$.