{"id":"https://openalex.org/W1997044393","doi":"https://doi.org/10.1109/tit.2014.2321280","title":"A Family of Optimal Locally Recoverable Codes","display_name":"A Family of Optimal Locally Recoverable Codes","publication_year":2014,"publication_date":"2014-05-23","ids":{"openalex":"https://openalex.org/W1997044393","doi":"https://doi.org/10.1109/tit.2014.2321280","mag":"1997044393"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2014.2321280","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2321280","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/1311.3284","any_repository_has_fulltext":true},"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/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":true,"raw_author_name":"Itzhak Tamo","raw_affiliation_strings":["#N#        University of Maryland, USA"],"affiliations":[{"raw_affiliation_string":"#N#        University of Maryland, USA","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004622357","display_name":"Alexander Barg","orcid":"https://orcid.org/0000-0002-8972-4413"},"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":"Alexander Barg","raw_affiliation_strings":["#N#        University of Maryland, USA"],"affiliations":[{"raw_affiliation_string":"#N#        University of Maryland, USA","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5085150941"],"corresponding_institution_ids":["https://openalex.org/I66946132"],"apc_list":null,"apc_paid":null,"fwci":67.2667,"has_fulltext":false,"cited_by_count":597,"citation_normalized_percentile":{"value":0.99943262,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"60","issue":"8","first_page":"4661","last_page":"4676"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11181","display_name":"Advanced Data Storage Technologies","score":1.0,"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":1.0,"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":0.9869999885559082,"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/T11130","display_name":"Coding theory and cryptography","score":0.9763000011444092,"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/code-word","display_name":"Code word","score":0.7787407040596008},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.7592487335205078},{"id":"https://openalex.org/keywords/locality","display_name":"Locality","score":0.6272497773170471},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.6251742243766785},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.578039288520813},{"id":"https://openalex.org/keywords/polynomial-code","display_name":"Polynomial code","score":0.5440707206726074},{"id":"https://openalex.org/keywords/symbol","display_name":"Symbol (formal)","score":0.5318856835365295},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.5312008261680603},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5307559967041016},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.48768365383148193},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45526719093322754},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4535275101661682},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4509831666946411},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.44601184129714966},{"id":"https://openalex.org/keywords/prefix-code","display_name":"Prefix code","score":0.44158199429512024},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.43623289465904236},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4284440279006958},{"id":"https://openalex.org/keywords/reed\u2013muller-code","display_name":"Reed\u2013Muller code","score":0.4186446964740753},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3820013999938965},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.37909823656082153},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34321898221969604},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3331851363182068},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.10616058111190796}],"concepts":[{"id":"https://openalex.org/C153207627","wikidata":"https://www.wikidata.org/wiki/Q863873","display_name":"Code word","level":3,"score":0.7787407040596008},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.7592487335205078},{"id":"https://openalex.org/C2779808786","wikidata":"https://www.wikidata.org/wiki/Q6664603","display_name":"Locality","level":2,"score":0.6272497773170471},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.6251742243766785},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.578039288520813},{"id":"https://openalex.org/C39635130","wikidata":"https://www.wikidata.org/wiki/Q7226636","display_name":"Polynomial code","level":5,"score":0.5440707206726074},{"id":"https://openalex.org/C134400042","wikidata":"https://www.wikidata.org/wiki/Q2372244","display_name":"Symbol (formal)","level":2,"score":0.5318856835365295},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.5312008261680603},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5307559967041016},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.48768365383148193},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45526719093322754},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4535275101661682},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4509831666946411},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.44601184129714966},{"id":"https://openalex.org/C20079647","wikidata":"https://www.wikidata.org/wiki/Q1278039","display_name":"Prefix code","level":5,"score":0.44158199429512024},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43623289465904236},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4284440279006958},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.4186446964740753},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3820013999938965},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.37909823656082153},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34321898221969604},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3331851363182068},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.10616058111190796},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","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":2,"locations":[{"id":"doi:10.1109/tit.2014.2321280","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2321280","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:1311.3284","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1311.3284","pdf_url":"https://arxiv.org/pdf/1311.3284","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1311.3284","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1311.3284","pdf_url":"https://arxiv.org/pdf/1311.3284","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.4699999988079071,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W197831480","https://openalex.org/W1529946666","https://openalex.org/W1606480398","https://openalex.org/W1968528796","https://openalex.org/W1977073502","https://openalex.org/W1993830711","https://openalex.org/W1995147907","https://openalex.org/W2006551665","https://openalex.org/W2008976700","https://openalex.org/W2021662392","https://openalex.org/W2050413942","https://openalex.org/W2050500290","https://openalex.org/W2060646539","https://openalex.org/W2061649200","https://openalex.org/W2065465262","https://openalex.org/W2068871408","https://openalex.org/W2069026918","https://openalex.org/W2080339104","https://openalex.org/W2099837838","https://openalex.org/W2105185344","https://openalex.org/W2124961791","https://openalex.org/W2126067205","https://openalex.org/W2126295689","https://openalex.org/W2139703052","https://openalex.org/W2140420067","https://openalex.org/W2150777202","https://openalex.org/W2167592273","https://openalex.org/W2170681444","https://openalex.org/W2171486154","https://openalex.org/W2625724326","https://openalex.org/W2949514404","https://openalex.org/W2963120590","https://openalex.org/W2963178700","https://openalex.org/W2977322974","https://openalex.org/W3101824114","https://openalex.org/W3103425664","https://openalex.org/W3106482607","https://openalex.org/W6607934843"],"related_works":["https://openalex.org/W2887855805","https://openalex.org/W2048714908","https://openalex.org/W83984714","https://openalex.org/W2293846540","https://openalex.org/W2157678969","https://openalex.org/W1998728561","https://openalex.org/W4237217078","https://openalex.org/W4214485061","https://openalex.org/W645598334","https://openalex.org/W1482626664"],"abstract_inverted_index":{"A":[0],"code":[1,54,75,90,96,107],"over":[2,66,117],"a":[3,18,21,34,49,67,73,148],"finite":[4,68],"alphabet":[5,97],"is":[6,17,83,101,112],"called":[7],"locally":[8],"recoverable":[9],"(LRC)":[10],"if":[11,76],"every":[12,132],"symbol":[13,150],"in":[14],"the":[15,41,46,77,89,95,106,137,156],"encoding":[16],"function":[19],"of":[20,36,45,62,94,147,155,163],"small":[22],"number":[23],"(at":[24],"most":[25,99],"<i":[26,80,118],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[27,81,119],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">r</i>":[28,82,120],")":[29],"other":[30],"symbols.":[31],"We":[32,122],"present":[33],"family":[35],"LRC":[37],"codes":[38,125],"that":[39],"attain":[40],"maximum":[42],"possible":[43],"value":[44],"distance":[47],"for":[48,98,131],"given":[50],"locality":[51,78],"parameter":[52,79],"and":[53,70,143],"cardinality.":[55],"The":[56,92,109],"codewords":[57],"are":[58],"obtained":[59],"as":[60],"evaluations":[61],"specially":[63],"constructed":[64],"polynomials":[65],"field,":[69],"reduce":[71],"to":[72,85,88,139],"Reed-Solomon":[74],"set":[84],"be":[86],"equal":[87],"dimension.":[91],"size":[93],"parameters":[100],"only":[102],"slightly":[103],"greater":[104],"than":[105],"length.":[108],"recovery":[110,145],"procedure":[111],"performed":[113],"by":[114,151],"polynomial":[115],"interpolation":[116],"points.":[121],"also":[123],"construct":[124],"with":[126],"several":[127,141],"disjoint":[128],"recovering":[129],"sets":[130],"symbol.":[133],"This":[134,158],"construction":[135],"enables":[136,160],"system":[138],"conduct":[140],"independent":[142],"simultaneous":[144],"processes":[146],"specific":[149],"accessing":[152],"different":[153],"parts":[154],"codeword.":[157],"property":[159],"high":[161],"availability":[162],"frequently":[164],"accessed":[165],"data":[166],"(\u201chot":[167],"data\u201d).":[168]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":36},{"year":2024,"cited_by_count":45},{"year":2023,"cited_by_count":32},{"year":2022,"cited_by_count":54},{"year":2021,"cited_by_count":39},{"year":2020,"cited_by_count":69},{"year":2019,"cited_by_count":61},{"year":2018,"cited_by_count":68},{"year":2017,"cited_by_count":74},{"year":2016,"cited_by_count":57},{"year":2015,"cited_by_count":43},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}