A Framework of Constructions of Minimal Storage Regenerating Codes with the Optimal Access/Update Property

In this paper, we present a generic framework for constructing systematic minimum storage regenerating codes with two parity nodes based on the invariant subspace technique. Codes constructed in our framework not only contain some best known codes as special cases, but also include some new codes with key properties such as the optimal access property and the optimal update property. In particular, for a given storage capacity of an individual node, one of the new codes has the largest number of systematic nodes and two of the new codes have the largest number of systematic nodes with the optimal update property.