On k-Partitioning the n-Cube

Let an edge cut partition the vertex set of the n-cube into κ subsets A1,..., A k with ∥Ai¦ — ¦Aj∥ ⩽ 1. We consider the problem to determine minimal size of such a cut and present its asymptotic as n, k → ∞ and also as n → ∞ and k is a constant of the form κ=2a±2b with a≥b≥0.