DC FieldValueLanguage
dc.contributor.authorDück, Natalia-
dc.contributor.authorZimmermann, Karl-Heinz-
dc.date.accessioned2019-06-24T12:36:00Z-
dc.date.available2019-06-24T12:36:00Z-
dc.date.issued2013-
dc.identifier.citationInternational Journal of Pure and Applied Mathematics 2 (86): 345-358 (2013)de_DE
dc.identifier.issn1314-3395de_DE
dc.identifier.urihttp://hdl.handle.net/11420/2808-
dc.description.abstractEach linear code can be described by a code ideal given as the sum of a toric ideal and a non-prime ideal. In this way, several concepts from the theory of toric ideals can be translated into the setting of code ideals. It will be shown that after adjusting some of these concepts, the same inclusion relationship between the set of circuits, the universal Gröbner basis and the Graver basis holds. Furthermore, in the case of binary linear codes, the universal Gröbner basis will consist of all binomials which correspond to codewords that satisfy the Singleton bound and a particular rank condition. This will give rise to a new class of binary linear codes denoted as Singleton codes. © 2013 Academic Publications, Ltd.en
dc.language.isoende_DE
dc.publisherAcademic Publishingde_DE
dc.relation.ispartofInternational journal of pure and applied mathematicsde_DE
dc.subjectlinear codede_DE
dc.subjectGröbner basisde_DE
dc.subjectuniversal Gröbner basisde_DE
dc.subjectGraver basisde_DE
dc.subjectcircuitde_DE
dc.subjecttoric idealde_DE
dc.subjectSingleton codede_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleUniversal Gröbner bases for binary linear codesde_DE
dc.typeArticlede_DE
dc.type.diniarticle-
dc.subject.ddccode510-
dcterms.DCMITypeText-
tuhh.abstract.englishEach linear code can be described by a code ideal given as the sum of a toric ideal and a non-prime ideal. In this way, several concepts from the theory of toric ideals can be translated into the setting of code ideals. It will be shown that after adjusting some of these concepts, the same inclusion relationship between the set of circuits, the universal Gröbner basis and the Graver basis holds. Furthermore, in the case of binary linear codes, the universal Gröbner basis will consist of all binomials which correspond to codewords that satisfy the Singleton bound and a particular rank condition. This will give rise to a new class of binary linear codes denoted as Singleton codes. © 2013 Academic Publications, Ltd.de_DE
tuhh.publisher.doi10.12732/ijpam.v86i2.9-
tuhh.publication.instituteEingebettete Systeme E-13de_DE
tuhh.type.opus(wissenschaftlicher) Artikel-
tuhh.institute.germanEingebettete Systeme E-13de
tuhh.institute.englishEingebettete Systeme E-13de_DE
tuhh.gvk.hasppnfalse-
dc.type.driverarticle-
dc.type.casraiJournal Article-
tuhh.container.issue2de_DE
tuhh.container.volume86de_DE
tuhh.container.startpage345de_DE
tuhh.container.endpage358de_DE
item.fulltextNo Fulltext-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.creatorOrcidDück, Natalia-
item.creatorOrcidZimmermann, Karl-Heinz-
item.languageiso639-1en-
item.cerifentitytypePublications-
item.openairetypeArticle-
item.grantfulltextnone-
item.creatorGNDDück, Natalia-
item.creatorGNDZimmermann, Karl-Heinz-
crisitem.author.deptEingebettete Systeme E-13-
crisitem.author.deptEingebettete Systeme E-13-
crisitem.author.orcid0000-0002-0819-1345-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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