Enumeration of Generalized Necklaces over Finite Fields

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dc.contributor.author Algallaf, Jumah Ali
dc.date.accessioned 2016-04-28T21:24:32Z
dc.date.available 2016-04-28T21:24:32Z
dc.date.copyright 2016 en_US
dc.date.issued 2016-04-28
dc.identifier.uri http://hdl.handle.net/1828/7227
dc.description.abstract In 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.language.iso en en_US
dc.rights Available to the World Wide Web en_US
dc.rights.uri http://creativecommons.org/licenses/by-nd/2.5/ca/ *
dc.subject Generalized Necklaces en_US
dc.subject Finite Field en_US
dc.subject QC codes en_US
dc.subject QT codes en_US
dc.title Enumeration of Generalized Necklaces over Finite Fields en_US
dc.type project en_US
dc.contributor.supervisor Gulliver, T. Aaron
dc.degree.department Department of Electrical and Computer Engineering en_US
dc.degree.level Master of Engineering M.Eng. en_US
dc.description.scholarlevel Graduate en_US

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