Erde's path-decomposition conjecture for hypercubes

Let $Q_n$ be the $n$-dimensional hypercube, with edge set of size $n2^{n-1}$. A path decomposition of $Q_n$ is a decomposition of its edge set into paths of a common length. Erde's conjecture. For even $n$, if $r$ divides $n2^{n-1}$ and $r<2^n$, then a path of length $r$ decomposes $Q_n$. The conjecture generalizes known path decompositions arising from cycle decompositions; the source proves the cases $r=2n,4n,\ldots,2^{m-1}n$ when $n\geq 2^m$, but the full statement remains open.