Enumeration of Generalized Necklaces over Finite Fields

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dc.contributor.authorAlgallaf, Jumah Ali
dc.contributor.supervisorGulliver, T. Aaron
dc.date.accessioned2016-04-28T21:24:32Z
dc.date.available2016-04-28T21:24:32Z
dc.date.copyright2016en_US
dc.date.issued2016-04-28
dc.degree.departmentDepartment of Electrical and Computer Engineeringen_US
dc.degree.levelMaster of Engineering M.Eng.en_US
dc.description.abstractIn combinatorial theory, a necklace is an equivalence class of a word under cyclic shift. Enumerating necklaces over a finite field F_q is an essential yet time-consuming step in constructing Quasi-Cyclic (QC) and Quasi-Twisted (QT) codes. QC and QT codes are important subclasses of linear block codes which can be characterized in terms of m×m circulant and twistulant matrices, respectively. Circulant and twistulant matrices have been used extensively in the construction of error correcting codes and many of the best-known linear codes have been obtained using constructions based on theses matrices. In this project, a generalization of necklaces which is related to circulant and twistulant matrices is presented along with a closed form expression to count their numbers. The goal is to enumerate these generalized necklaces over prime and prime power fields using MATLAB.en_US
dc.description.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/7227
dc.language.isoenen_US
dc.rightsAvailable to the World Wide Weben_US
dc.rights.urihttp://creativecommons.org/licenses/by-nd/2.5/ca/*
dc.subjectGeneralized Necklacesen_US
dc.subjectFinite Fielden_US
dc.subjectQC codesen_US
dc.subjectQT codesen_US
dc.titleEnumeration of Generalized Necklaces over Finite Fieldsen_US
dc.typeprojecten_US

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