{"id":"https://openalex.org/W2000645537","doi":"https://doi.org/10.1109/tit.2014.2298234","title":"Some Bounds on the Size of Codes","display_name":"Some Bounds on the Size of Codes","publication_year":2014,"publication_date":"2014-01-31","ids":{"openalex":"https://openalex.org/W2000645537","doi":"https://doi.org/10.1109/tit.2014.2298234","mag":"2000645537"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2014.2298234","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2298234","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/1206.6006","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Emanuele Bellini","orcid":null},"institutions":[{"id":"https://openalex.org/I193223587","display_name":"University of Trento","ror":"https://ror.org/05trd4x28","country_code":"IT","type":"education","lineage":["https://openalex.org/I193223587"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Emanuele Bellini","raw_affiliation_strings":["University of Trento, Trento, Italy"],"affiliations":[{"raw_affiliation_string":"University of Trento, Trento, Italy","institution_ids":["https://openalex.org/I193223587"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Eleonora Guerrini","orcid":null},"institutions":[{"id":"https://openalex.org/I4210101743","display_name":"Laboratoire d'Informatique, de Robotique et de Micro\u00e9lectronique de Montpellier","ror":"https://ror.org/013yean28","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I151295451","https://openalex.org/I19894307","https://openalex.org/I4210101743","https://openalex.org/I4210159245","https://openalex.org/I4412460525"]},{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Eleonora Guerrini","raw_affiliation_strings":["University of Montpellier 2, Laboratory of Informatics, Robotics, and Microelectronics, Montpellier, France"],"affiliations":[{"raw_affiliation_string":"University of Montpellier 2, Laboratory of Informatics, Robotics, and Microelectronics, Montpellier, France","institution_ids":["https://openalex.org/I4210101743","https://openalex.org/I19894307"]}]},{"author_position":"last","author":{"id":null,"display_name":"Massimiliano Sala","orcid":null},"institutions":[{"id":"https://openalex.org/I193223587","display_name":"University of Trento","ror":"https://ror.org/05trd4x28","country_code":"IT","type":"education","lineage":["https://openalex.org/I193223587"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Massimiliano Sala","raw_affiliation_strings":["University of Trento, Trento, Italy"],"affiliations":[{"raw_affiliation_string":"University of Trento, Trento, Italy","institution_ids":["https://openalex.org/I193223587"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I193223587"],"apc_list":null,"apc_paid":null,"fwci":0.4243,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.73886657,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"60","issue":"3","first_page":"1475","last_page":"1480"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.3978999853134155,"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":0.3978999853134155,"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":0.29989999532699585,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.042100001126527786,"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7648000121116638},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.48750001192092896},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.45249998569488525},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.41449999809265137},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.373199999332428},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.32280001044273376}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7648000121116638},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6608999967575073},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5473999977111816},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5102999806404114},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.48750001192092896},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.45249998569488525},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.41449999809265137},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.373199999332428},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33410000801086426},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.32280001044273376},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.3174000084400177},{"id":"https://openalex.org/C93693863","wikidata":"https://www.wikidata.org/wiki/Q897659","display_name":"Branch and bound","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C108509264","wikidata":"https://www.wikidata.org/wiki/Q5420758","display_name":"Expander code","level":5,"score":0.267300009727478}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2014.2298234","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2298234","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:1206.6006","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1206.6006","pdf_url":"https://arxiv.org/pdf/1206.6006","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:HAL:lirmm-01282040v1","is_oa":false,"landing_page_url":"https://hal-lirmm.ccsd.cnrs.fr/lirmm-01282040","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory, 2014, 60 (3), pp.1475-1480. ⟨10.1109/TIT.2014.2298234⟩","raw_type":"Journal articles"},{"id":"pmh:oai:iris.unitn.it:11572/33016","is_oa":false,"landing_page_url":"http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6704275&tag=1","pdf_url":null,"source":{"id":"https://openalex.org/S4306401913","display_name":"Institutional Research Information System (Universit\u00e0 degli Studi di Trento)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193223587","host_organization_name":"University of Trento","host_organization_lineage":["https://openalex.org/I193223587"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1206.6006","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1206.6006","pdf_url":"https://arxiv.org/pdf/1206.6006","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":11,"referenced_works":["https://openalex.org/W1911679041","https://openalex.org/W1965097372","https://openalex.org/W1999270946","https://openalex.org/W2066583820","https://openalex.org/W2073098064","https://openalex.org/W2104385491","https://openalex.org/W2109937605","https://openalex.org/W2142293082","https://openalex.org/W2170716519","https://openalex.org/W4206775542","https://openalex.org/W6604469142"],"related_works":[],"abstract_inverted_index":{"We":[0],"present":[1],"some":[2,102],"upper":[3,84],"bounds":[4,21,70],"on":[5,104],"the":[6,30,33,36,46,66,72,87,96],"size":[7],"of":[8,24,40,45,53],"nonlinear":[9,88],"codes":[10,16],"and":[11,17,39,59,100],"their":[12],"restriction":[13],"to":[14],"systematic":[15],"linear":[18,41,67,97],"codes.":[19],"These":[20],"are":[22,109],"independent":[23],"other":[25,82],"known":[26],"theoretical":[27],"bounds,":[28],"e.g.,":[29],"Griesmer":[31],"bound,":[32,35,38],"Johnson":[34],"Plotkin":[37],"programming":[42,98],"bounds.":[43,85,115],"One":[44],"new":[47,121],"bound":[48,55,94,99,122],"is":[49],"actually":[50],"an":[51],"improvement":[52],"a":[54,76,120],"by":[56],"Zinoviev,":[57],"Litsyn,":[58],"Laihonen.":[60],"Our":[61],"experiments":[62],"show":[63,106],"that":[64,107],"in":[65,75,123],"case":[68],"our":[69,93],"provide":[71],"best":[73],"value":[74],"wide":[77],"range,":[78],"compared":[79],"with":[80,95,101],"all":[81],"closed-formula":[83],"In":[86,116],"case,":[89],"we":[90,112,118],"also":[91],"compare":[92],"improvements":[103],"it,":[105],"there":[108],"cases":[110],"where":[111],"beat":[113],"these":[114],"particular,":[117],"obtain":[119],"Brouwer's":[124],"table":[125],"for":[126],"A3(16,3).":[127]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}