Constructing CSS-T Codes from Extended Quasi-Cyclic Codes

We 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.

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

2025

Author dc:creator

• George, Ross Patrick

Chair dc:contributor.committeechair

• Matthews, Gretchen L.

Committee members dc:contributor.committeemember

• Lopez Valdez, Hiram Habid
• Camps Moreno, Eduardo
• Cotardo, Giuseppe

• Coding Theory
• CSS-T Codes
• Quasi-Cyclic Codes
• Quantum Codes

Statement dc:rights

• Creative Commons Attribution 4.0 International

Licence dc:rights.uri

• http://creativecommons.org/licenses/by/4.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:44208

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/135085