  The piggybacking framework for designing erasure codes for distributed
storage has empirically proven to be very useful, and has been used to design
codes with desirable properties, such as low repair bandwidth and complexity.
However, the theoretical properties of this framework remain largely
unexplored. We address this by adapting a general characterization of repair
schemes (previously used for Reed Solomon codes) to analyze piggybacking codes
with low substriping. With this characterization, we establish a separation
between piggybacking and general erasure codes, and several impossibility
results for subcategories of piggybacking codes; for certain parameters, we
also present explicit, optimal constructions of piggybacking codes.
