Valvo, Daniel William2020-06-112020-06-112020-06-10vt_gsexam:26553http://hdl.handle.net/10919/98818In 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.ETDIn CopyrightCartesian codeReed-Solomon codeexact repair schemesfinite fieldsdistributed storage networksmultivariate polynomialsThesis