{"id":"https://openalex.org/W4237389945","doi":"https://doi.org/10.1109/tit.2021.3134201","title":"A Generalization of the Cylinder Conjecture for Divisible Codes","display_name":"A Generalization of the Cylinder Conjecture for Divisible Codes","publication_year":2021,"publication_date":"2021-12-09","ids":{"openalex":"https://openalex.org/W4237389945","doi":"https://doi.org/10.1109/tit.2021.3134201"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3134201","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3134201","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2011.02923","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014779065","display_name":"Sascha Kurz","orcid":"https://orcid.org/0000-0003-4597-2041"},"institutions":[{"id":"https://openalex.org/I54009628","display_name":"University of Bayreuth","ror":"https://ror.org/0234wmv40","country_code":"DE","type":"education","lineage":["https://openalex.org/I54009628"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Sascha Kurz","raw_affiliation_strings":["Department of Mathematics, University of Bayreuth, Bayreuth, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Bayreuth, Bayreuth, Germany","institution_ids":["https://openalex.org/I54009628"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032358511","display_name":"Sam Mattheus","orcid":"https://orcid.org/0000-0001-9062-2062"},"institutions":[{"id":"https://openalex.org/I13469542","display_name":"Vrije Universiteit Brussel","ror":"https://ror.org/006e5kg04","country_code":"BE","type":"education","lineage":["https://openalex.org/I13469542"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Sam Mattheus","raw_affiliation_strings":["Department of Mathematics and Data Science, Vrije Universiteit Brussel, Elsene, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Data Science, Vrije Universiteit Brussel, Elsene, Belgium","institution_ids":["https://openalex.org/I13469542"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014779065"],"corresponding_institution_ids":["https://openalex.org/I54009628"],"apc_list":null,"apc_paid":null,"fwci":0.4079,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70438189,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"68","issue":"4","first_page":"2281","last_page":"2289"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7765827178955078},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6792033910751343},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.6041464805603027},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5863868594169617},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47213298082351685},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39159953594207764},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.10539701581001282},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09115096926689148}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7765827178955078},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6792033910751343},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6041464805603027},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5863868594169617},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47213298082351685},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39159953594207764},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.10539701581001282},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09115096926689148}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2021.3134201","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3134201","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2011.02923","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.02923","pdf_url":"https://arxiv.org/pdf/2011.02923","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:eref.uni-bayreuth.de:68965","is_oa":false,"landing_page_url":"https://eref.uni-bayreuth.de/68965/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196442","display_name":"ERef Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Artikel in einer Zeitschrift"},{"id":"pmh:oai:vubissmart:VUBISSMART:2000:158390","is_oa":false,"landing_page_url":"https://biblio.vub.ac.be/vubir/a-generalization-of-the-cylinder-conjecture-for-divisible-codes(3d0420c5-6fe0-4448-97bb-b373c4e15596).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306402573","display_name":"VUBIR (Vrije Universiteit Brussel)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I13469542","host_organization_name":"Vrije Universiteit Brussel","host_organization_lineage":["https://openalex.org/I13469542"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2011.02923","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.02923","pdf_url":"https://arxiv.org/pdf/2011.02923","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W190248387","https://openalex.org/W594967076","https://openalex.org/W1512937197","https://openalex.org/W1569612250","https://openalex.org/W1997833576","https://openalex.org/W2085970350","https://openalex.org/W2555021951","https://openalex.org/W2896218262","https://openalex.org/W2963915107","https://openalex.org/W4287991930","https://openalex.org/W6607754618","https://openalex.org/W6772131190"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2504004674","https://openalex.org/W1987679298","https://openalex.org/W2963177394","https://openalex.org/W4313359513","https://openalex.org/W2498744856","https://openalex.org/W4390482104","https://openalex.org/W322408318","https://openalex.org/W149041114","https://openalex.org/W4302778552"],"abstract_inverted_index":{"We":[0],"extend":[1],"the":[2,14,47,66,100,115],"original":[3,101],"cylinder":[4,67,102],"conjecture":[5,103],"on":[6],"point":[7],"sets":[8],"in":[9],"affine":[10],"three-dimensional":[11],"space":[12],"to":[13],"more":[15],"general":[16],"framework":[17],"of":[18,37,50,65,84],"divisible":[19],"linear":[20,38],"codes":[21],"over":[22],"<inline-formula":[23,85,105,119],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[24,86,106,120],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[25,87,107,121],"<tex-math":[26,88,108,122],"notation=\"LaTeX\">${":[27],"{\\mathbb":[28],"{F}}_{q}}$":[29],"</tex-math></inline-formula>":[30,90,112,126],"and":[31,42,77,113],"their":[32],"classification.":[33],"Through":[34],"a":[35,59,63,96],"mix":[36],"programming,":[39],"combinatorial":[40],"techniques":[41],"computer":[43],"enumeration,":[44],"we":[45,56,94],"investigate":[46],"structural":[48],"properties":[49],"these":[51],"codes.":[52],"In":[53,92],"this":[54],"way,":[55],"can":[57],"prove":[58,78],"reduction":[60],"theorem":[61],"for":[62,81,99,104,118],"generalization":[64],"conjecture,":[68],"show":[69],"some":[70],"instances":[71],"where":[72],"it":[73],"does":[74],"not":[75],"hold":[76],"its":[79],"validity":[80],"small":[82],"values":[83],"notation=\"LaTeX\">$q$":[89],".":[91,127],"particular,":[93],"correct":[95],"flawed":[97],"proof":[98,117],"notation=\"LaTeX\">$q":[109,123],"=":[110,124],"5$":[111],"present":[114],"first":[116],"7$":[125]},"counts_by_year":[{"year":2023,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
