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Classes of Convolutional Codes and Their Applications
Kumar, Viraj S.
Kumar, Viraj S.
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).
Abstract
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.