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dc.contributor.advisorVoloch, José Felipeen
dc.creatorCharters, Philippa Lianaen
dc.date.accessioned2011-06-13T15:07:41Zen
dc.date.available2011-06-13T15:07:41Zen
dc.date.issued2009-05en
dc.identifier.urihttp://hdl.handle.net/2152/11667en
dc.descriptiontexten
dc.description.abstractIn this paper, we provide a generalization of binary quadratic residue codes to the cases of higher power prime residues over the finite field of the same order, which we will call qth power residue codes. We find generating polynomials for such codes, define a new notion corresponding to the binary concept of an idempotent, and use this to find square root lower bound for the codeword weight of the duals of such codes, which leads to a lower bound on the weight of the codewords themselves. In addition, we construct a family of asymptotically bad qth power residue codes.en
dc.format.mediumelectronicen
dc.language.isoengen
dc.rightsCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.en
dc.subjectBinary quadratic residue codesen
dc.subjectHigher power prime residuesen
dc.subjectFinite fielden
dc.subjectResidue codesen
dc.subjectIdempotenten
dc.titleGeneralizing binary quadratic residue codes to higher power residues over larger fieldsen
dc.description.departmentMathematicsen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorThe University of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen


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