{"id":"https://openalex.org/W1715633553","doi":"https://doi.org/10.1109/tit.2016.2518663","title":"Bounds on the Parameters of Locally Recoverable Codes","display_name":"Bounds on the Parameters of Locally Recoverable Codes","publication_year":2016,"publication_date":"2016-01-18","ids":{"openalex":"https://openalex.org/W1715633553","doi":"https://doi.org/10.1109/tit.2016.2518663","mag":"1715633553"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2016.2518663","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2518663","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085150941","display_name":"Itzhak Tamo","orcid":"https://orcid.org/0000-0002-8000-0419"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]},{"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":["IL","US"],"is_corresponding":true,"raw_author_name":"Itzhak Tamo","raw_affiliation_strings":["Department of Electrical Engineering-Systems, Tel Aviv University, Tel Aviv, Israel","Institute for Systems Research, University of Maryland, College Park, MD, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering-Systems, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Institute for Systems Research, University of Maryland, College Park, MD, USA","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004622357","display_name":"Alexander Barg","orcid":"https://orcid.org/0000-0002-8972-4413"},"institutions":[{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"government","lineage":["https://openalex.org/I1313323035"]},{"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, University of Maryland, College Park, MD, USA","Russian Academy of Sciences, IITP, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, USA","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"Russian Academy of Sciences, IITP, Moscow, Russia","institution_ids":["https://openalex.org/I1313323035"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008712753","display_name":"Alexey Frolov","orcid":"https://orcid.org/0000-0002-6734-0179"},"institutions":[{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"government","lineage":["https://openalex.org/I1313323035"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Alexey Frolov","raw_affiliation_strings":["Russian Academy of Sciences, IITP, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Russian Academy of Sciences, IITP, Moscow, Russia","institution_ids":["https://openalex.org/I1313323035"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5085150941"],"corresponding_institution_ids":["https://openalex.org/I16391192","https://openalex.org/I66946132"],"apc_list":null,"apc_paid":null,"fwci":18.3887,"has_fulltext":false,"cited_by_count":142,"citation_normalized_percentile":{"value":0.9937227,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"62","issue":"6","first_page":"3070","last_page":"3083"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11181","display_name":"Advanced Data Storage Technologies","score":0.9998999834060669,"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/T11181","display_name":"Advanced Data Storage Technologies","score":0.9998999834060669,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9714999794960022,"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"}},{"id":"https://openalex.org/T11478","display_name":"Caching and Content Delivery","score":0.9552000164985657,"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":0.6636950969696045},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6632847785949707},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6181550621986389},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5645800828933716},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.5190780162811279},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.512103796005249},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5081164836883545},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.4795496165752411},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4658653736114502},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.4567284882068634},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4123043715953827},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.26277846097946167},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25742602348327637},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22593572735786438}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6636950969696045},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6632847785949707},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6181550621986389},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5645800828933716},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.5190780162811279},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.512103796005249},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5081164836883545},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.4795496165752411},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4658653736114502},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4567284882068634},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4123043715953827},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.26277846097946167},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25742602348327637},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22593572735786438},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2016.2518663","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2518663","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3492167673","display_name":null,"funder_award_id":"CCF1217245","funder_id":"https://openalex.org/F4320332170","funder_display_name":"Directorate for Engineering"},{"id":"https://openalex.org/G3729223212","display_name":null,"funder_award_id":"14-50-00150","funder_id":"https://openalex.org/F4320324099","funder_display_name":"Russian Science Foundation"},{"id":"https://openalex.org/G4341719754","display_name":null,"funder_award_id":"CCF1422955","funder_id":"https://openalex.org/F4320332170","funder_display_name":"Directorate for Engineering"},{"id":"https://openalex.org/G8063919833","display_name":null,"funder_award_id":"CCF1217894","funder_id":"https://openalex.org/F4320332170","funder_display_name":"Directorate for Engineering"}],"funders":[{"id":"https://openalex.org/F4320324099","display_name":"Russian Science Foundation","ror":"https://ror.org/03y2gwe85"},{"id":"https://openalex.org/F4320332170","display_name":"Directorate for Engineering","ror":"https://ror.org/00b6sbb32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1536930200","https://openalex.org/W1575622900","https://openalex.org/W1582254841","https://openalex.org/W1678309266","https://openalex.org/W1778950143","https://openalex.org/W1957362188","https://openalex.org/W1993830711","https://openalex.org/W1995147907","https://openalex.org/W1997044393","https://openalex.org/W2006551665","https://openalex.org/W2014149071","https://openalex.org/W2018102393","https://openalex.org/W2021662392","https://openalex.org/W2034215849","https://openalex.org/W2037127812","https://openalex.org/W2057922111","https://openalex.org/W2060646539","https://openalex.org/W2073529360","https://openalex.org/W2080132708","https://openalex.org/W2080339104","https://openalex.org/W2092614961","https://openalex.org/W2126067205","https://openalex.org/W2128765501","https://openalex.org/W2131486878","https://openalex.org/W2141042196","https://openalex.org/W2155418912","https://openalex.org/W2242452602","https://openalex.org/W2320835389","https://openalex.org/W2550412208","https://openalex.org/W2567264041","https://openalex.org/W2953303692","https://openalex.org/W2962735098","https://openalex.org/W2963120590","https://openalex.org/W2963754206","https://openalex.org/W2963944222","https://openalex.org/W3100004208","https://openalex.org/W3100282565","https://openalex.org/W3100522903","https://openalex.org/W3104191667","https://openalex.org/W3106534456","https://openalex.org/W4300188436","https://openalex.org/W6678581137"],"related_works":["https://openalex.org/W135568846","https://openalex.org/W2460434904","https://openalex.org/W1789159349","https://openalex.org/W2113911300","https://openalex.org/W2151857680","https://openalex.org/W4386066307","https://openalex.org/W832867880","https://openalex.org/W917159298","https://openalex.org/W1975697476","https://openalex.org/W3136820369"],"abstract_inverted_index":{"A":[0],"locally":[1],"recoverable":[2],"code":[3,8],"(LRC":[4],"code)":[5],"is":[6,20],"a":[7,10,21,24,32,55,111],"over":[9],"finite":[11],"alphabet,":[12],"such":[13],"that":[14,30],"every":[15,60,97],"symbol":[16],"in":[17],"the":[18,46,74,100,115,129,132],"encoding":[19],"function":[22],"of":[23,27,48,79,102,134],"small":[25],"number":[26],"other":[28],"symbols":[29],"form":[31],"recovering":[33,57,94,104,139],"set.":[34],"In":[35],"this":[36],"paper,":[37],"we":[38,62,109,122],"derive":[39,63,110,124],"new":[40],"finite-length":[41,125],"and":[42,72,131],"asymptotic":[43,65],"bounds":[44,127],"on":[45,114,128],"parameters":[47,116],"LRC":[49,52,70,82,89,135],"codes.":[50,83],"For":[51,99],"codes":[53,71,90,136],"with":[54,91,137],"single":[56],"set":[58],"for":[59,69,88,96],"coordinate,":[61],"an":[64],"Gilbert-Varshamov":[66],"type":[67],"bound":[68,113],"find":[73],"maximum":[75],"attainable":[76],"relative":[77],"distance":[78,133],"asymptotically":[80],"good":[81],"Similar":[84],"results":[85],"are":[86],"established":[87],"two":[92],"disjoint":[93],"sets":[95,105],"coordinate.":[98],"case":[101],"multiple":[103,138],"(the":[106],"availability":[107],"problem),":[108],"lower":[112],"using":[117],"expander":[118],"graph":[119],"arguments.":[120],"Finally,":[121],"also":[123],"upper":[126],"rate":[130],"sets.":[140]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":21},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":20},{"year":2017,"cited_by_count":20},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}