Regenerating codes with generalized conditions of reconstruction and regeneration

As a distributed storage system with regenerating function of failed nodes, regenerating codes have been studied recently. In a [n, k, d]-regenerating codes framework, a message can be reconstructed from any subsets of k nodes out of n nodes and any failed nodes can be repaired from any subsets of d nodes out of (n - 1) nodes. The conditions of the reconstruction and regeneration can be generalized. In this paper, we propose the regenerating codes with generalized conditions and derive their optimal constructing algorithm under the multiple assignment map construction framework. The optimal codes of the framework are obtained by solving integer programming problems in a similar way of generalized secret sharing scheme's construction based on a multiple assignment map.