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dc.contributor.advisorJohnsen, Trygve
dc.contributor.advisorVerdure, Hugues
dc.contributor.authorKarpova, Anna
dc.date.accessioned2015-06-11T12:47:33Z
dc.date.available2015-06-11T12:47:33Z
dc.date.issued2015-05-15
dc.description.abstractIn this thesis we first give a survey of linear error-correcting codes, and how many of their most important properties only depend on the matroids derived from their parity check matrices. We also introduce the Stanley-Reisner ring associated to the simplicial complex of the independent sets of a matroid. We then recall in particular how some important properties of linear codes, including their generalized weight polynomials, are dependent only on the Z-graded Betti numbers for the Stanley-Reisner rings of their associated matroids, and the so-called elongations of these matroids. We will use this fact to find the generalized weight polynomials of simplex codes and Reed-Muller codes of the first order.en_US
dc.identifier.urihttps://hdl.handle.net/10037/7737
dc.identifier.urnURN:NBN:no-uit_munin_7325
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.titleHomological methods applied to theory of codes and matroidsen_US
dc.typeMaster thesisen_US
dc.typeMastergradsoppgaveen_US


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Attribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC-SA 3.0)
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC-SA 3.0)