DC FieldValueLanguage
dc.contributor.authorStelldinger, Peer-
dc.date.accessioned2024-11-18T12:57:49Z-
dc.date.available2024-11-18T12:57:49Z-
dc.date.issued2025-02-27-
dc.identifier.issn0097-3165en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12738/16530-
dc.description.abstractDe Bruijn tori, also called perfect maps, are two-dimensional periodic arrays of letters drawn from a given finite alphabet, such that each possible pattern of a given shape (m,n) appears exactly once within one period of the torus. It is still unknown if de Bruijn tori of some certain size exist, like e.g. square shaped de Bruijn Tori with odd m=n in {3,5,7} and an even alphabet size k. However, in certain applications like positional coding, sub-perfect maps are sufficient, i.e. one does not need every possible (m,n)-pattern to appear, as long as a sufficient large number of such patterns is captured and every pattern occurs at most once. We show, that given any m=n and a square alphabet size k², one can efficiently construct a sub-perfect map which is almost perfect, i.e. of almost maximal size. We do this by introducing de Bruijn rings, i.e. sub-perfect maps of minimal height, and providing an efficient construction method for them. We extend our results to non-square torus shapes and arbitrary non-prime alphabet sizes.en
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.relation.ispartofJournal of combinatorial theory : JCTA. Series Aen_US
dc.subjectDe Bruijn torusen_US
dc.subjectDe Bruijn ringen_US
dc.subjectPerfect mapen_US
dc.subjectSub-perfect mapen_US
dc.subject.ddc004: Informatiken_US
dc.titleOn de Bruijn Rings and families of almost perfect mapsen
dc.title.alternativeÜber de Bruijn Ringe und fast perfekte Kartende
dc.typeArticleen_US
dc.description.versionPeerRevieweden_US
tuhh.container.volume214en_US
tuhh.oai.showtrueen_US
tuhh.publication.instituteForschungs- und Transferzentrum Smart Systemsen_US
tuhh.publication.instituteDepartment Informatiken_US
tuhh.publication.instituteFakultät Technik und Informatiken_US
tuhh.publisher.doi10.1016/j.jcta.2025.106030-
tuhh.publisher.doi10.48550/arXiv.2405.03309-
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.rights.cchttps://creativecommons.org/licenses/by/4.0/en_US
dc.type.casraiJournal Article-
dc.type.diniarticle-
dc.type.driverarticle-
dc.type.statusinfo:eu-repo/semantics/publishedVersionen_US
dcterms.DCMITypeText-
local.comment.externalPreprint: https://doi.org/10.48550/arXiv.2405.03309. Verlagsversion: https://doi.org/10.1016/j.jcta.2025.106030.en_US
item.grantfulltextnone-
item.creatorGNDStelldinger, Peer-
item.cerifentitytypePublications-
item.creatorOrcidStelldinger, Peer-
item.languageiso639-1en-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.fulltextNo Fulltext-
item.openairetypeArticle-
crisitem.author.deptDepartment Informatik-
crisitem.author.orcid0000-0001-8079-2797-
crisitem.author.parentorgFakultät Technik und Informatik-
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