Classes of Convolutional Codes and Their Applications
A Master of Science in Mathematics by Viraj S. Kumar entitled, “Classes of Convolutional Codes and Their Applications”, submitted in September 2025. Thesis advisor is Dr. Taher Abualrub. Soft copy is available (Thesis, Completion Certificate, Approval Signatures, and AUS Archives Consent Form).
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | doctoralThesis |
| منشور في: |
2025
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| الموضوعات: | |
| الوصول للمادة أونلاين: | https://hdl.handle.net/11073/32511 |
| الوسوم: |
إضافة وسم
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| _version_ | 1864513441998307328 |
|---|---|
| author | Kumar, Viraj S. |
| author_facet | Kumar, Viraj S. |
| author_role | author |
| dc.contributor.none.fl_str_mv | Abualrub, Taher |
| dc.creator.none.fl_str_mv | Kumar, Viraj S. |
| dc.date.none.fl_str_mv | 2025-11-26T05:56:23Z 2025-11-26T05:56:23Z 2025-09 |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | 29.232-2025.18 https://hdl.handle.net/11073/32511 |
| dc.language.none.fl_str_mv | en_US |
| dc.relation.none.fl_str_mv | Master of Science in Mathematics (MSMTH) |
| dc.subject.none.fl_str_mv | Convolutional codes Cyclic convolutional codes Skew-cyclic convolutional codes Skew polynomial rings Ore extensions |
| dc.title.none.fl_str_mv | Classes of Convolutional Codes and Their Applications |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/doctoralThesis |
| description | A Master of Science in Mathematics by Viraj S. Kumar entitled, “Classes of Convolutional Codes and Their Applications”, submitted in September 2025. Thesis advisor is Dr. Taher Abualrub. Soft copy is available (Thesis, Completion Certificate, Approval Signatures, and AUS Archives Consent Form). |
| format | doctoralThesis |
| id | aus_47e62f596ee18fde71e447833683cdb0 |
| identifier_str_mv | 29.232-2025.18 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/32511 |
| publishDate | 2025 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Classes of Convolutional Codes and Their ApplicationsKumar, Viraj S.Convolutional codesCyclic convolutional codesSkew-cyclic convolutional codesSkew polynomial ringsOre extensionsA Master of Science in Mathematics by Viraj S. Kumar entitled, “Classes of Convolutional Codes and Their Applications”, submitted in September 2025. Thesis advisor is Dr. Taher Abualrub. Soft copy is available (Thesis, Completion Certificate, Approval Signatures, and AUS Archives Consent Form).In this thesis, formulations of cyclicity of convolutional codes are examined. A brief introduction to linear, cyclic and convolutional codes is given, followed by a review of two formulations of cyclicity for convolutional codes in the literature, -cyclicity and skew-cyclicity. Next, two new generalizations of skew-cyclic convolutional codes are constructed by broadening the class of underlying skew-polynomial rings. The properties of these generalized codes including generator polynomials, generating idempotents, and duality are investigated. Lastly, several computational examples are constructed.College of Arts and SciencesDepartment of Mathematics and StatisticsMaster of Science in Mathematics (MSMTH)Abualrub, Taher2025-11-26T05:56:23Z2025-11-26T05:56:23Z2025-09info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdf29.232-2025.18https://hdl.handle.net/11073/32511en_USMaster of Science in Mathematics (MSMTH)oai:repository.aus.edu:11073/325112025-11-26T11:34:21Z |
| spellingShingle | Classes of Convolutional Codes and Their Applications Kumar, Viraj S. Convolutional codes Cyclic convolutional codes Skew-cyclic convolutional codes Skew polynomial rings Ore extensions |
| status_str | publishedVersion |
| title | Classes of Convolutional Codes and Their Applications |
| title_full | Classes of Convolutional Codes and Their Applications |
| title_fullStr | Classes of Convolutional Codes and Their Applications |
| title_full_unstemmed | Classes of Convolutional Codes and Their Applications |
| title_short | Classes of Convolutional Codes and Their Applications |
| title_sort | Classes of Convolutional Codes and Their Applications |
| topic | Convolutional codes Cyclic convolutional codes Skew-cyclic convolutional codes Skew polynomial rings Ore extensions |
| url | https://hdl.handle.net/11073/32511 |