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dc.contributor.authorJohnsen, Trygve
dc.contributor.authorVerdure, Hugues
dc.date.accessioned2013-03-11T10:17:11Z
dc.date.available2013-03-11T10:17:11Z
dc.date.issued2013
dc.description.abstractTo each linear code C over a finite field we associate the matroid M(C) of its parity check matrix. For any matroid M one can define its generalized Hamming weights, and if a matroid is associated to such a parity check matrix, and thus of type M(C) , these weights are the same as those of the code C . In our main result we show how the weights d1,…,dk of a matroid M are determined by the N -graded Betti numbers of the Stanley–Reisner ring of the simplicial complex whose faces are the independent sets of M , and derive some consequences. We also give examples which give negative results concerning other types of (global) Betti numbers, and using other examples we show that the generalized Hamming weights do not in general determine the N -graded Betti numbers of the Stanley–Reisner ring. The negative examples all come from matroids of type M(C).en
dc.identifier.citationApplicable Algebra in Engineering, Communication and Computing 24(2013) nr. 1 s. 73-93en
dc.identifier.cristinIDFRIDAID 998315
dc.identifier.doihttp://dx.doi.org/10.1007/s00200-012-0183-7
dc.identifier.issn0938-1279
dc.identifier.urihttps://hdl.handle.net/10037/4946
dc.identifier.urnURN:NBN:no-uit_munin_4647
dc.language.isoengen
dc.publisherSpringerlinken
dc.rights.accessRightsopenAccess
dc.subjectVDP::Mathematics and natural science: 400::Mathematics: 410::Algebra/algebraic analysis: 414en
dc.subjectVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410::Algebra/algebraisk analyse: 414en
dc.titleHamming weights and Betti numbers of Stanley–Reisner rings associated to matroidsen
dc.typeJournal articleen
dc.typeTidsskriftartikkelen
dc.typePeer revieweden


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