Constructing CSS-T Codes from Extended Quasi-Cyclic Codes

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dc.contributor.authorGeorge, Ross Patricken
dc.contributor.committeechairMatthews, Gretchen L.en
dc.contributor.committeememberLopez Valdez, Hiram Habiden
dc.contributor.committeememberCamps Moreno, Eduardoen
dc.contributor.committeememberCotardo, Giuseppeen
dc.contributor.departmentMathematicsen
dc.date.accessioned2025-06-06T08:01:17Zen
dc.date.available2025-06-06T08:01:17Zen
dc.date.issued2025-06-05en
dc.description.abstractWe analyze a construction of quasi-cyclic codes in an extension field based on the polynomials which generate the corresponding codes in the base fields. We establish a set of code operations on which trace relationships between extended quasi-cyclic codes are the same as the operations taken on the original codes. We also discuss how these relationships can be used to construct CSS-T codes for quantum-error correction.en
dc.description.abstractgeneralWe study a construction of classical error-correcting codes which is unaffected by shifting actions and how those codes can be used to construct codes useful for error-correction in quantum computing.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:44208en
dc.identifier.urihttps://hdl.handle.net/10919/135085en
dc.language.isoenen
dc.publisherVirginia Techen
dc.rightsCreative Commons Attribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.subjectCoding Theoryen
dc.subjectCSS-T Codesen
dc.subjectQuasi-Cyclic Codesen
dc.subjectQuantum Codesen
dc.titleConstructing CSS-T Codes from Extended Quasi-Cyclic Codesen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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