{"id":"https://openalex.org/W2762711634","doi":"https://doi.org/10.1109/tit.2010.2094812","title":"On the Number of Errors Correctable with Codes on Graphs","display_name":"On the Number of Errors Correctable with Codes on Graphs","publication_year":2011,"publication_date":"2011-01-21","ids":{"openalex":"https://openalex.org/W2762711634","doi":"https://doi.org/10.1109/tit.2010.2094812","mag":"2762711634"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2010.2094812","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2094812","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/0911.4522","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Alexander Barg","orcid":null},"institutions":[{"id":"https://openalex.org/I4210107660","display_name":"Institute for Information Transmission Problems","ror":"https://ror.org/013w2d378","country_code":"RU","type":"facility","lineage":["https://openalex.org/I4210107660"]},{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["RU","US"],"is_corresponding":false,"raw_author_name":"Alexander Barg","raw_affiliation_strings":["Department of Electrical and Computer Engineering and with the Institute for Systems Research, University of Maryland, College Park, MD, USA","Institute for Problems of Information Transmission, Moscow, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering and with the Institute for Systems Research, University of Maryland, College Park, MD, USA","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"Institute for Problems of Information Transmission, Moscow, Russia","institution_ids":["https://openalex.org/I4210107660"]}]},{"author_position":"last","author":{"id":null,"display_name":"Arya Mazumdar","orcid":null},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Arya Mazumdar","raw_affiliation_strings":["Department of Electrical and Computer Engineering and with the Institute for Systems Research, University of Maryland, College Park, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering and with the Institute for Systems Research, University of Maryland, College Park, MD, USA","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0035,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.89010065,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"57","issue":"2","first_page":"910","last_page":"919"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.574999988079071,"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"}},"topics":[{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.574999988079071,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.24770000576972961,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.018400000408291817,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/hamming-code","display_name":"Hamming code","score":0.6617000102996826},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.6133000254631042},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.6000999808311462},{"id":"https://openalex.org/keywords/expander-code","display_name":"Expander code","score":0.5426999926567078},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.5360999703407288},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.4970000088214874},{"id":"https://openalex.org/keywords/concatenation","display_name":"Concatenation (mathematics)","score":0.48919999599456787},{"id":"https://openalex.org/keywords/reed\u2013muller-code","display_name":"Reed\u2013Muller code","score":0.46320000290870667},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.43320000171661377}],"concepts":[{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.6617000102996826},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.6133000254631042},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6103000044822693},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.6000999808311462},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5501000285148621},{"id":"https://openalex.org/C108509264","wikidata":"https://www.wikidata.org/wiki/Q5420758","display_name":"Expander code","level":5,"score":0.5426999926567078},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.5360999703407288},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5092999935150146},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.4970000088214874},{"id":"https://openalex.org/C87619178","wikidata":"https://www.wikidata.org/wiki/Q126002","display_name":"Concatenation (mathematics)","level":2,"score":0.48919999599456787},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.46320000290870667},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.43320000171661377},{"id":"https://openalex.org/C159246509","wikidata":"https://www.wikidata.org/wiki/Q5428725","display_name":"Factor graph","level":3,"score":0.40869998931884766},{"id":"https://openalex.org/C87117866","wikidata":"https://www.wikidata.org/wiki/Q7683664","display_name":"Tanner graph","level":5,"score":0.4032000005245209},{"id":"https://openalex.org/C29696283","wikidata":"https://www.wikidata.org/wiki/Q369440","display_name":"Hamming graph","level":5,"score":0.38609999418258667},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.3447999954223633},{"id":"https://openalex.org/C114504821","wikidata":"https://www.wikidata.org/wiki/Q2164281","display_name":"Turbo code","level":3,"score":0.33480000495910645},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.33000001311302185},{"id":"https://openalex.org/C128151799","wikidata":"https://www.wikidata.org/wiki/Q13563306","display_name":"Luby transform code","level":5,"score":0.3296000063419342},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.31850001215934753},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.31130000948905945},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.29249998927116394},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2888999879360199},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.2874999940395355},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2732999920845032},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.27160000801086426},{"id":"https://openalex.org/C13251829","wikidata":"https://www.wikidata.org/wiki/Q3085841","display_name":"Dense graph","level":5,"score":0.2508000135421753}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2010.2094812","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2094812","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:0911.4522","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0911.4522","pdf_url":"https://arxiv.org/pdf/0911.4522","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0911.4522","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0911.4522","pdf_url":"https://arxiv.org/pdf/0911.4522","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2762711634.pdf","grobid_xml":"https://content.openalex.org/works/W2762711634.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1970912697","https://openalex.org/W2005606852","https://openalex.org/W2036878392","https://openalex.org/W2051569409","https://openalex.org/W2128139208","https://openalex.org/W2130458083","https://openalex.org/W2133068391","https://openalex.org/W2158843246","https://openalex.org/W2170758137","https://openalex.org/W2171486154","https://openalex.org/W2293231900","https://openalex.org/W2567264041","https://openalex.org/W3100522903","https://openalex.org/W4300188436"],"related_works":[],"abstract_inverted_index":{"We":[0,48],"study":[1],"ensembles":[2,41],"of":[3,37,59,80,108],"codes":[4,26,38,52,75,82,85,99,110],"on":[5,27,101],"graphs":[6,16],"(generalized":[7],"low-density":[8],"parity-check,":[9],"or":[10],"LDPC":[11],"codes)":[12],"constructed":[13,76],"from":[14],"random":[15],"and":[17,22,83,104],"fixed":[18],"local":[19,109],"constrained":[20],"codes,":[21],"their":[23,116],"extension":[24],"to":[25,74,115],"hypergraphs.":[28],"It":[29],"is":[30],"known":[31,91],"that":[32,50,70,93],"the":[33,45,106],"average":[34],"minimum":[35,88],"distance":[36,113],"in":[39],"these":[40,51],"grows":[42],"linearly":[43,56],"with":[44,86,111],"code":[46],"length.":[47,117],"show":[49,69],"can":[53],"correct":[54],"a":[55],"growing":[57],"number":[58],"errors":[60],"under":[61],"simple":[62],"iterative":[63],"decoding":[64],"algorithms.":[65],"In":[66],"particular,":[67],"we":[68],"this":[71,95],"property":[72,96],"extends":[73],"by":[77],"parallel":[78],"concatenation":[79],"Hamming":[81],"other":[84],"small":[87],"distance.":[89],"Previously":[90],"results":[92],"proved":[94],"for":[97],"graph":[98,102],"relied":[100],"expansion":[103],"required":[105],"choice":[107],"large":[112],"relative":[114]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2017-10-20T00:00:00"}