  We adapt (over $\mathbb{F}_2$) the general notions of multiplicative
function, Dirichlet convolution and Inverse. We get some interesting results,
namely necessary conditions for an odd binary polynomial to be perfect. Note
that we are inspired by the "analogous" works in \cite{Gall-Rahav-newcongr} and
\cite{Touchard}, about odd perfect numbers.
