  We investigate the distributions of quantum coherence characterized by
superadditivity relations in multipartite quantum systems. General
superadditivity inequalities based on the $\alpha$th ($\alpha\geqslant 1$)
power of $l_1$ norm of coherence are presented for multiqubit states, which
include the existing ones as special cases. Our result is shown to be tighter
than the existing one by a specific example.
