A brief survey of self-dual codes

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dc.contributor.advisorVoloch, Jose Felipeen
dc.contributor.advisorHelleloid, Geir T.en
dc.creatorOktavia, Rinien
dc.date.accessioned2010-06-04T14:43:28Zen
dc.date.accessioned2017-05-11T22:19:53Z
dc.date.available2010-06-04T14:43:28Zen
dc.date.available2017-05-11T22:19:53Z
dc.date.issued2009-08en
dc.date.submittedAugust 2009en
dc.descriptiontexten
dc.description.abstractThis report is a survey of self-dual binary codes. We present the fundamental MacWilliams identity and Gleason’s theorem on self-dual binary codes. We also examine the upper bound of minimum weights of self-dual binary codes using the extremal weight enumerator formula. We describe the shadow code of a self-dual code and the restrictions of the weight enumerator of the shadow code. Then using the restrictions, we calculate the weight enumerators of self-dual codes of length 38 and 40 and we obtain the known weight enumerators of this lengths. Finally, we investigate the Gaborit-Otmani experimental construction of selfdual binary codes. This construction involves a fixed orthogonal matrix, and we compare the result to the results obtained using other orthogonal matrices.en
dc.description.departmentMathematicsen
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/2152/ETD-UT-2009-08-189en
dc.language.isoengen
dc.subjectSelf-Dual Codesen
dc.subjectWeight Enumeratoren
dc.subjectMacWilliams Identityen
dc.subjectGleason's Theorem on Self-Dual Codesen
dc.subjectMinimum Distanceen
dc.titleA brief survey of self-dual codesen
dc.type.genrethesisen

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