Scalable codes with locality and availability derived from tessellation via [7, 3, 4] Simplex code graph

A new family of scalable codes with locality and availability for information repair in data storage systems for e-health applications was presented recently. The construction was based on a graph of the [7, 3, 4] Simplex code. In this paper it is shown that the construction can be generalized via tessellation in a Euclidian plane. The codes obtained have new interesting recoverability properties. They can in some cases repair damage to many storage nodes in multiple connected graphs via sequential decoding, which is similar to healing wounds in biological systems. The advantages of the original codes, namely the availability, functionality, efficiency and high data accessibility, will be preserved also in these new codes. The computational complexity and communication costs of their incrementation will remain constant and modest. These codes could be adapted to disaster recovery because it is straightforward to place the nodes so that the graph is easily mapped on a real structure in space.