Repairing Cartesian Codes with Linear Exact Repair Schemes

Abstract

In this paper, we develop a scheme to recover a single erasure when using a Cartesian code,in the context of a distributed storage system. Particularly, we develop a scheme withconsiderations to minimize the associated bandwidth and maximize the associateddimension. The problem of recovering a missing node's data exactly in a distributedstorage system is known as theexact repair problem. Previous research has studied theexact repair problem for Reed-Solomon codes. We focus on Cartesian codes, and show wecan enact the recovery using a linear exact repair scheme framework, similar to the oneoutlined by Guruswami and Wooters in 2017.