Distributed storage systems are studied in the presence of an active omniscient adversary. The adversary is able to control several storage nodes in the system and alter their behavior. A Polytope code is proposed to handle such an adversary, and it is used to prove a lower bound on the overall storage capacity. Polytope codes have been shown to outperform linear codes over a finite field in defeating active adversaries. In a Polytope code, linear operations are performed over the integers rather than a finite field. This allows examinations of cross-covariances as a sort of parity check, which can improve error detection and correction without sacrificing asymptotic rate.
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