Decompositions of \(n\)-Cube into \(2^mn\)-Cycles

It is known that the \(n\)-dimensional hypercube \(Q_n,\) for \(n\) even, has a decomposition into \(k\)-cycles for \(k=n, 2n,\) \(2^l\) with \(2 \leq l \leq n.\) In this paper, we prove that \(Q_n\) has a decomposition into \(2^mn\)-cycles for \(n \geq 2^m.\) As an immediate consequence of this result, we get path decompositions of \(Q_n\) as well. This gives a partial solution to a conjecture posed by Ramras and also, it solves some special cases of a conjecture due to Erde.