Constructing Double-Erasure HoVer Codes Using Latin Squares

Storage applications are in urgent need of multi-erasure codes. But there is no consensus on the best coding technique. Hafner has presented a class of multi-erasure codes named HoVer codes [1]. This kind of codes has a unique data/parity layout which provides a range of implementation options that cover a large portion of the performance/efficiency trade-off space. Thus it can be applied to many scenarios by simple tuning. In this paper, we give a combinatorial representation of a family of double-erasure HoVer codes - create a mapping between this family of codes and Latin squares. We also present two families of double-erasure HoVer codes respectively based on the column-Hamiltonian Latin squares (of odd order) and a family of Latin squares of even order. Compared with the double-erasure HoVer codes presented in [1], the new codes enable greater flexibility in performance and efficiency trade-off.