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Towers of Betti Numbers of Matroids and Weight Distribution of Linear Codes and their Duals

dc.contributor.advisorVerdure, Hugues
dc.contributor.advisorJohnsen, Trygve
dc.contributor.authorHuerga Represa, Violeta
dc.date.accessioned2015-06-11T12:32:21Z
dc.date.available2015-06-11T12:32:21Z
dc.date.issued2015-05-15
dc.description.abstractThe main notion behind the study of matroids is linear dependence. In this thesis, we give a survey of the concepts and properties of linear error-correcting codes over finite fields being dependent only on the matroids derived from these codes. In particular, the weight distributions of linear codes, and their extensions, over bigger fields are only dependent on the N-graded Betti numbers of these matroids and their so-called elongations. We will use this fact to find the weight distributions for some important codes as constant weight codes and Hamming codes. In addition, the connection between the Betti tower of a matroid and its dual tower will be studied for general matroids.en_US
dc.identifier.urihttps://hdl.handle.net/10037/7736
dc.identifier.urnURN:NBN:no-uit_munin_7324
dc.language.isoengen_US
dc.publisherUiT Norges arktiske universiteten_US
dc.publisherUiT The Arctic University of Norwayen_US
dc.rights.accessRightsopenAccess
dc.rights.holderCopyright 2015 The Author(s)
dc.rights.urihttps://creativecommons.org/licenses/by-nc-sa/3.0en_US
dc.rightsAttribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC-SA 3.0)en_US
dc.subject.courseIDMAT-3900en_US
dc.subjectVDP::Mathematics and natural science: 400::Mathematics: 410::Algebra/algebraic analysis: 414en_US
dc.subjectAlgebraic Combinatoricsen_US
dc.subjectVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410::Algebra/algebraisk analyse: 414en_US
dc.titleTowers of Betti Numbers of Matroids and Weight Distribution of Linear Codes and their Dualsen_US
dc.typeMaster thesisen_US
dc.typeMastergradsoppgaveen_US


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