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In distributed storage systems that employ erasure coding, the issue of minimizing the total repair bandwidth required to exactly regenerate a storage node after a failure arises. This repair bandwidth depends on the structure of the storage code and the repair strategies used to restore the lost data. Minimizing it requires that undesired data during a repair align in the smallest possible spaces, using the concept of Interference Alignment (IA). Here, a points-on-a-lattice representation of the symbol extension IA of Cadambe et al. provides cues to perfect IA instances which the authors combine with fundamental properties of Hadamard matrices to construct a new storage code with favorable repair properties.
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