{"id":"https://openalex.org/W2623918255","doi":"https://doi.org/10.1109/tit.2017.2713245","title":"New Constructions of Optimal Locally Recoverable Codes via Good Polynomials","display_name":"New Constructions of Optimal Locally Recoverable Codes via Good Polynomials","publication_year":2017,"publication_date":"2017-06-07","ids":{"openalex":"https://openalex.org/W2623918255","doi":"https://doi.org/10.1109/tit.2017.2713245","mag":"2623918255"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2017.2713245","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2713245","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/A5101424400","display_name":"Jian Liu","orcid":"https://orcid.org/0000-0002-7557-8347"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jian Liu","raw_affiliation_strings":["School of Computer Software, Tianjin University, Tianjin, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Software, Tianjin University, Tianjin, China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034752358","display_name":"Sihem Mesnager","orcid":"https://orcid.org/0000-0003-4008-2031"},"institutions":[{"id":"https://openalex.org/I12356871","display_name":"T\u00e9l\u00e9com Paris","ror":"https://ror.org/01naq7912","country_code":"FR","type":"education","lineage":["https://openalex.org/I12356871","https://openalex.org/I205703379","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I48825208","display_name":"Universit\u00e9 Paris 8","ror":"https://ror.org/04wez5e68","country_code":"FR","type":"education","lineage":["https://openalex.org/I48825208"]},{"id":"https://openalex.org/I4210091279","display_name":"Universit\u00e9 Sorbonne Paris Nord","ror":"https://ror.org/0199hds37","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210091279"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210102686","display_name":"Laboratoire Analyse, G\u00e9om\u00e9trie et Applications","ror":"https://ror.org/018nzqy79","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210091279","https://openalex.org/I4210102686","https://openalex.org/I4210141950","https://openalex.org/I48825208"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Sihem Mesnager","raw_affiliation_strings":["Department of Mathematics, University of Paris VIII, Saint-Denis, France","T\u00e9l\u00e9com ParisTech, Paris, France","UMR 7539, CNRS, Laboratory of Analysis, Geometry and Applications, University of Paris XIII, Villetaneuse, France"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Paris VIII, Saint-Denis, France","institution_ids":["https://openalex.org/I48825208"]},{"raw_affiliation_string":"T\u00e9l\u00e9com ParisTech, Paris, France","institution_ids":["https://openalex.org/I12356871"]},{"raw_affiliation_string":"UMR 7539, CNRS, Laboratory of Analysis, Geometry and Applications, University of Paris XIII, Villetaneuse, France","institution_ids":["https://openalex.org/I4210102686","https://openalex.org/I204730241","https://openalex.org/I4210091279","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080997578","display_name":"Lusheng Chen","orcid":"https://orcid.org/0000-0002-3921-0318"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lusheng Chen","raw_affiliation_strings":["School of Mathematical Sciences, Nankai University, Tianjin, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Nankai University, Tianjin, China","institution_ids":["https://openalex.org/I205237279"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101424400"],"corresponding_institution_ids":["https://openalex.org/I162868743"],"apc_list":null,"apc_paid":null,"fwci":4.9728,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.95826046,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"64","issue":"2","first_page":"889","last_page":"899"},"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/T11130","display_name":"Coding theory and cryptography","score":0.989799976348877,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9746999740600586,"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/mathematics","display_name":"Mathematics","score":0.7669628262519836},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.667100191116333},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5301564335823059},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5218787789344788},{"id":"https://openalex.org/keywords/locality","display_name":"Locality","score":0.5036987662315369},{"id":"https://openalex.org/keywords/reed\u2013muller-code","display_name":"Reed\u2013Muller code","score":0.4896398186683655},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.4783191978931427},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.45497584342956543},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4462260603904724},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.41254496574401855},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.3632343113422394},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17889297008514404},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.13748818635940552},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13276085257530212},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.12035477161407471},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.08263057470321655}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7669628262519836},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.667100191116333},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5301564335823059},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5218787789344788},{"id":"https://openalex.org/C2779808786","wikidata":"https://www.wikidata.org/wiki/Q6664603","display_name":"Locality","level":2,"score":0.5036987662315369},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.4896398186683655},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.4783191978931427},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.45497584342956543},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4462260603904724},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.41254496574401855},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.3632343113422394},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17889297008514404},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.13748818635940552},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13276085257530212},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.12035477161407471},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.08263057470321655},{"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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2017.2713245","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2713245","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:HAL:hal-03958968v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03958968","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, 2018, 64 (2), pp.889-899. ⟨10.1109/TIT.2017.2713245⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W27322304","https://openalex.org/W1570424847","https://openalex.org/W1638607647","https://openalex.org/W1639538057","https://openalex.org/W1707811365","https://openalex.org/W1957362188","https://openalex.org/W1987787762","https://openalex.org/W1993830711","https://openalex.org/W1997044393","https://openalex.org/W2006551665","https://openalex.org/W2017346026","https://openalex.org/W2021662392","https://openalex.org/W2022619326","https://openalex.org/W2031058522","https://openalex.org/W2049581867","https://openalex.org/W2050413942","https://openalex.org/W2050500290","https://openalex.org/W2062509897","https://openalex.org/W2155418912","https://openalex.org/W2335546159","https://openalex.org/W2962735098","https://openalex.org/W2963944222","https://openalex.org/W3099613636","https://openalex.org/W3100004208","https://openalex.org/W3102225876","https://openalex.org/W3104944838"],"related_works":["https://openalex.org/W2293846540","https://openalex.org/W4386066307","https://openalex.org/W4248142543","https://openalex.org/W4383466497","https://openalex.org/W1992135520","https://openalex.org/W1798117689","https://openalex.org/W2095450438","https://openalex.org/W4237217078","https://openalex.org/W3136820369","https://openalex.org/W1632494370"],"abstract_inverted_index":{"In":[0,94,128],"recent":[1],"literature,":[2],"a":[3,55],"family":[4],"of":[5,49,60,67,79,106,116,124],"optimal":[6,33,81,125,140],"linear":[7,34],"locally":[8],"recoverable":[9],"codes":[10,36,83,145],"(LRC":[11],"codes)":[12],"that":[13],"attain":[14],"the":[15,38,47,50,77,136,159],"maximum":[16],"possible":[17],"distance":[18],"(given":[19],"code":[20,160],"length,":[21],"cardinality,":[22],"and":[23,76],"locality)":[24],"is":[25,37,44,91,157],"presented.":[26],"The":[27],"key":[28],"ingredient":[29],"for":[30,71,87,148],"constructing":[31,80],"such":[32],"LRC":[35,51,82,126,144],"so-called":[39],"r-good":[40,61,117],"polynomials,":[41,109],"where":[42,155],"r":[43,152],"equal":[45],"to":[46,112],"locality":[48,90],"code.":[52],"However,":[53],"given":[54,89],"prime":[56],"p,":[57],"known":[58],"constructions":[59,115,123],"polynomials":[62,120,132],"over":[63,84,146],"some":[64,72],"extension":[65],"field":[66,86],"Fp":[68],"exist":[69],"only":[70],"special":[73],"integers":[74,151],"r,":[75],"problem":[78],"small":[85],"any":[88],"still":[92],"open.":[93],"this":[95],"paper,":[96],"by":[97],"using":[98],"function":[99],"composition,":[100],"we":[101],"present":[102],"two":[103],"general":[104],"methods":[105],"designing":[107],"good":[108],"which":[110],"lead":[111],"three":[113],"new":[114,122],"polynomials.":[118],"Such":[119],"bring":[121],"codes.":[127],"particular,":[129],"our":[130],"constructed":[131],"as":[133,135,153],"well":[134],"power":[137],"functions":[138],"yield":[139],"(n,":[141],"k,":[142],"r)":[143],"Fq":[147],"all":[149],"positive":[150],"localities,":[154],"q":[156],"near":[158],"length":[161],"n.":[162]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":8}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}