Multilinear algebra for distributed storage

Exact-repair regenerating codes (ERRCs) are a class of codes designed for distributed storage systems. A distributed storage system is a collection of devices that collaborate to store a large file. The collaboration is such that (a) if a user contacts sufficiently many devices, the user can recover the stored file; and (b) if one device fails, the remaining healthy devices can repair the failing device to maintain the properties (a) and (b). In this work, we focus on the trade-off among file size, device capacity, and the cost of repairing failing devices. We construct ERRCs with the same set of parameters as cascade codes. It has been conjectured that this set of parameters is optimal. Our construction relies on tensors and wedges and is purely algebraic. We discuss how the codes survive simultaneous device failures.