Hypercube 1-factorizations from extended Hamming codes

Based on the extended Hamming code, for n = 2 r we construct a proper edge-coloring of the n-dimensional hypercube Qn with n colors (i.e. 1-factorization) such that every edge has exactly one parallel edge from each color class except its own. Two edges are said to be parallel if they are opposite on a common 4-cycle. We study properties of this coloring and applications for some Turلn-type problems.