Two storage code constructions allowing partially collaborative repairs

We consider the problem of repairing simultaneously several node failures in a networked distributed storage system using erasure codes. While the notion of collaborative repair, where all nodes participating in the repair collaborate among each others, has been studied, we propose two code constructions that illustrate that the repair could be invoking instead different levels of collaboration, which we call partial collaboration. We consider extreme cases: when the storage, respectively the repair bandwidth, are minimum.