Repairing Cartesian Codes with Linear Exact Repair Schemes

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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2020

Author dc:creator

• Valvo, Daniel William

Chair dc:contributor.committeechair

• Matthews, Gretchen L.

Committee members dc:contributor.committeemember

• Mihalcea, Constantin Leonardo
• Orr, Daniel D.

• Cartesian code
• Reed-Solomon code
• exact repair schemes
• finite fields
• distributed storage networks
• multivariate polynomials

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:26553

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/98818