{"id":"https://openalex.org/W4378649699","doi":"https://doi.org/10.1007/s10623-023-01236-2","title":"Densities of codes of various linearity degrees in translation-invariant metric spaces","display_name":"Densities of codes of various linearity degrees in translation-invariant metric spaces","publication_year":2023,"publication_date":"2023-05-29","ids":{"openalex":"https://openalex.org/W4378649699","doi":"https://doi.org/10.1007/s10623-023-01236-2"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-023-01236-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-023-01236-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-023-01236-2.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10623-023-01236-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075442918","display_name":"Anina Gruica","orcid":"https://orcid.org/0009-0008-3066-3223"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Anina Gruica","raw_affiliation_strings":["Eindhoven University of Technology, Eindhoven, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Eindhoven University of Technology, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057606881","display_name":"Anna-Lena Trautmann","orcid":"https://orcid.org/0000-0003-2685-2343"},"institutions":[{"id":"https://openalex.org/I202963720","display_name":"University of St.Gallen","ror":"https://ror.org/0561a3s31","country_code":"CH","type":"education","lineage":["https://openalex.org/I202963720"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Anna-Lena Horlemann","raw_affiliation_strings":["University of St. Gallen, St. Gallen, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of St. Gallen, St. Gallen, Switzerland","institution_ids":["https://openalex.org/I202963720"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025356502","display_name":"Alberto Ravagnani","orcid":"https://orcid.org/0000-0001-5901-9484"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Alberto Ravagnani","raw_affiliation_strings":["Eindhoven University of Technology, Eindhoven, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Eindhoven University of Technology, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084030216","display_name":"Nadja Willenborg","orcid":"https://orcid.org/0000-0003-3049-7268"},"institutions":[{"id":"https://openalex.org/I202963720","display_name":"University of St.Gallen","ror":"https://ror.org/0561a3s31","country_code":"CH","type":"education","lineage":["https://openalex.org/I202963720"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Nadja Willenborg","raw_affiliation_strings":["University of St. Gallen, St. Gallen, Switzerland"],"raw_orcid":"https://orcid.org/0000-0003-3049-7268","affiliations":[{"raw_affiliation_string":"University of St. Gallen, St. Gallen, Switzerland","institution_ids":["https://openalex.org/I202963720"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5084030216"],"corresponding_institution_ids":["https://openalex.org/I202963720"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.7846,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.76643173,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"92","issue":"3","first_page":"609","last_page":"637"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11181","display_name":"Advanced Data Storage Technologies","score":0.9861999750137329,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/mathematics","display_name":"Mathematics","score":0.7248396873474121},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6626495718955994},{"id":"https://openalex.org/keywords/linearity","display_name":"Linearity","score":0.6557964086532593},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5822409987449646},{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.5484673380851746},{"id":"https://openalex.org/keywords/equivalence-of-metrics","display_name":"Equivalence of metrics","score":0.5068679451942444},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.47666671872138977},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.4322183132171631},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.42940109968185425},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4268399477005005},{"id":"https://openalex.org/keywords/intrinsic-metric","display_name":"Intrinsic metric","score":0.4176207482814789},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.41494330763816833},{"id":"https://openalex.org/keywords/convex-metric-space","display_name":"Convex metric space","score":0.36633622646331787},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32760298252105713},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.2722212076187134},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16156834363937378},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08958104252815247}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7248396873474121},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6626495718955994},{"id":"https://openalex.org/C77170095","wikidata":"https://www.wikidata.org/wiki/Q1753188","display_name":"Linearity","level":2,"score":0.6557964086532593},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5822409987449646},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.5484673380851746},{"id":"https://openalex.org/C191226916","wikidata":"https://www.wikidata.org/wiki/Q5384710","display_name":"Equivalence of metrics","level":4,"score":0.5068679451942444},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.47666671872138977},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.4322183132171631},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.42940109968185425},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4268399477005005},{"id":"https://openalex.org/C41261874","wikidata":"https://www.wikidata.org/wiki/Q3855712","display_name":"Intrinsic metric","level":4,"score":0.4176207482814789},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.41494330763816833},{"id":"https://openalex.org/C196613150","wikidata":"https://www.wikidata.org/wiki/Q3966092","display_name":"Convex metric space","level":3,"score":0.36633622646331787},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32760298252105713},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.2722212076187134},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16156834363937378},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08958104252815247},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10623-023-01236-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-023-01236-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-023-01236-2.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/0a07bab3-ba97-4113-abc6-3d53b22ca181","is_oa":true,"landing_page_url":"https://research.tue.nl/files/302014361/2208.10573v2.pdf","pdf_url":"https://pure.tue.nl/ws/files/302014361/2208.10573v2.pdf","source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Gruica, A, Horlemann, A-L, Ravagnani, A & Willenborg, N 2024, 'Densities of Codes of Various Linearity Degrees in Translation-Invariant Metric Spaces', Designs, Codes and Cryptography, vol. 92, no. 3, pp. 609-637. https://doi.org/10.1007/s10623-023-01236-2","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.tue.nl:openaire/0a07bab3-ba97-4113-abc6-3d53b22ca181","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/0a07bab3-ba97-4113-abc6-3d53b22ca181","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Gruica, A, Horlemann, A-L, Ravagnani, A & Willenborg, N 2024, 'Densities of Codes of Various Linearity Degrees in Translation-Invariant Metric Spaces', Designs, Codes and Cryptography, vol. 92, no. 3, pp. 609-637. https://doi.org/10.1007/s10623-023-01236-2","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.tue.nl:publications/0a07bab3-ba97-4113-abc6-3d53b22ca181","is_oa":true,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=85160437990&partnerID=8YFLogxK","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Gruica, A, Horlemann, A-L, Ravagnani, A & Willenborg, N 2024, 'Densities of Codes of Various Linearity Degrees in Translation-Invariant Metric Spaces', Designs, Codes and Cryptography, vol. 92, no. 3, pp. 609-637. https://doi.org/10.1007/s10623-023-01236-2","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10623-023-01236-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-023-01236-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-023-01236-2.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4099999964237213}],"awards":[{"id":"https://openalex.org/G5618363122","display_name":"Invariants of Rank-Metric Codes and Matrix Completions over GF(q) -- A Combinatorial Approach","funder_award_id":"VI.Vidi.203.045","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G660757063","display_name":"Structure and Asymptotic Density of Extremal Codes","funder_award_id":"OCENW.KLEIN.539","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4378649699.pdf"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1495716978","https://openalex.org/W1995875735","https://openalex.org/W2001841415","https://openalex.org/W2014944833","https://openalex.org/W2095547380","https://openalex.org/W2096667287","https://openalex.org/W2148575324","https://openalex.org/W2242479605","https://openalex.org/W2398693322","https://openalex.org/W2745281314","https://openalex.org/W2762207129","https://openalex.org/W2963761872","https://openalex.org/W2990083380","https://openalex.org/W3009813707","https://openalex.org/W3096146904","https://openalex.org/W3103202762","https://openalex.org/W3155530075","https://openalex.org/W3178595420","https://openalex.org/W3214034101","https://openalex.org/W3215859912","https://openalex.org/W4292806204","https://openalex.org/W4380875540"],"related_works":["https://openalex.org/W1996610422","https://openalex.org/W2947185879","https://openalex.org/W2795812777","https://openalex.org/W2389830804","https://openalex.org/W2088486639","https://openalex.org/W2565930412","https://openalex.org/W1493939247","https://openalex.org/W3103264541","https://openalex.org/W2963791829","https://openalex.org/W4378649699"],"abstract_inverted_index":{"Abstract":[0],"We":[1,22],"investigate":[2],"the":[3,25,39,43,48,55,63,68],"asymptotic":[4,56],"density":[5,57],"of":[6,28,58],"error-correcting":[7],"codes":[8,59],"with":[9],"good":[10],"distance":[11],"properties":[12],"and":[13,19,33,46,67],"prescribed":[14],"linearity":[15,65],"degree,":[16],"including":[17],"(sub)linear":[18],"nonlinear":[20],"codes.":[21],"focus":[23],"on":[24,62],"general":[26],"setting":[27],"finite":[29],"translation-invariant":[30],"metric":[31],"spaces,":[32],"then":[34],"specialize":[35],"our":[36],"results":[37,52],"to":[38,42,47],"Hamming":[40],"metric,":[41,45],"rank":[44],"sum-rank":[49],"metric.":[50,70],"Our":[51],"show":[53],"that":[54],"heavily":[60],"depends":[61],"imposed":[64],"degree":[66],"chosen":[69]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2023-05-30T00:00:00"}