Searching for Minimum Storage Regenerating Codes

Regenerating codes allow distributed storage systems to recover from the loss of a storage node while transmitting the minimum possible amount of data across the network. We search for examples of Minimum Storage Regenerating Codes. To exhaustively search the space of potential codes, we reduce the potential search space in several ways. We impose an additional symmetry condition on codes that we consider. We specify codes in a simple alternative way, using additional recovered coefficients rather than transmission coefficients. We place codes into equivalence classes to avoid redundant checking. We find MSR codes for the parameters n = 5 and k = 3 in various fields. We demonstrate that it is possible for such codes to be composed of vectors in general position.