Polytope codes for distributed storage in the presence of an active omniscient adversary

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.