  Genuineness and distillability of entanglement play a key role in quantum
information tasks, and they are easily disturbed by the noise. We construct a
family of multipartite states without genuine entanglement and distillability
sudden death across every bipartition, respectively. They are realized by
establishing the noise as the multipartite high dimensional Pauli channels.
Further, we construct a locally unitary channel as another noise such that the
multipartite Greenberger-Horne-Zeilinger state becomes the D{\"u}r's
multipartite state. We also show that the quantum information masking still
works under the noise we constructed, and thus show a novel quantum secret
sharing scheme under noise. The evolution of a family of three-qutrit genuinely
entangled states distillable across every bipartition under noise is also
investigated.
