{"id":"https://openalex.org/W2593205974","doi":"https://doi.org/10.1109/isit.2017.8006512","title":"On optimal ternary locally repairable codes","display_name":"On optimal ternary locally repairable codes","publication_year":2017,"publication_date":"2017-06-01","ids":{"openalex":"https://openalex.org/W2593205974","doi":"https://doi.org/10.1109/isit.2017.8006512","mag":"2593205974"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2017.8006512","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2017.8006512","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-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/A5042001449","display_name":"Jie Hao","orcid":"https://orcid.org/0000-0003-2032-665X"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]},{"id":"https://openalex.org/I3131625388","display_name":"University Town of Shenzhen","ror":"https://ror.org/05f5j6225","country_code":"CN","type":"education","lineage":["https://openalex.org/I3131625388"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jie Hao","raw_affiliation_strings":["Graduate School at Shenzhen, Tsinghua University, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"Graduate School at Shenzhen, Tsinghua University, Shenzhen, China","institution_ids":["https://openalex.org/I3131625388","https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034104790","display_name":"Shu\u2010Tao Xia","orcid":"https://orcid.org/0000-0002-8639-982X"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]},{"id":"https://openalex.org/I3131625388","display_name":"University Town of Shenzhen","ror":"https://ror.org/05f5j6225","country_code":"CN","type":"education","lineage":["https://openalex.org/I3131625388"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shu-Tao Xia","raw_affiliation_strings":["Graduate School at Shenzhen, Tsinghua University, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"Graduate School at Shenzhen, Tsinghua University, Shenzhen, China","institution_ids":["https://openalex.org/I3131625388","https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100427338","display_name":"Bin Chen","orcid":"https://orcid.org/0000-0002-4798-230X"},"institutions":[{"id":"https://openalex.org/I187400657","display_name":"South China Normal University","ror":"https://ror.org/01kq0pv72","country_code":"CN","type":"education","lineage":["https://openalex.org/I187400657"]},{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]},{"id":"https://openalex.org/I3131625388","display_name":"University Town of Shenzhen","ror":"https://ror.org/05f5j6225","country_code":"CN","type":"education","lineage":["https://openalex.org/I3131625388"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bin Chen","raw_affiliation_strings":["Graduate School at Shenzhen, Tsinghua University, Shenzhen, China","School of Mathematical Sciences, South China Normal University, Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"Graduate School at Shenzhen, Tsinghua University, Shenzhen, China","institution_ids":["https://openalex.org/I3131625388","https://openalex.org/I99065089"]},{"raw_affiliation_string":"School of Mathematical Sciences, South China Normal University, Guangzhou, China","institution_ids":["https://openalex.org/I187400657"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5042001449"],"corresponding_institution_ids":["https://openalex.org/I3131625388","https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":4.3852,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.94957773,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"171","last_page":"175"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11181","display_name":"Advanced Data Storage Technologies","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9988999962806702,"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":0.9972000122070312,"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/singleton","display_name":"Singleton","score":0.8365156650543213},{"id":"https://openalex.org/keywords/ternary-operation","display_name":"Ternary operation","score":0.7643488645553589},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6164684891700745},{"id":"https://openalex.org/keywords/parity-check-matrix","display_name":"Parity-check matrix","score":0.58788001537323},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5724128484725952},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5610584020614624},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"Minimum distance","score":0.5461626052856445},{"id":"https://openalex.org/keywords/locality","display_name":"Locality","score":0.5335807204246521},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.531654417514801},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47253111004829407},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3419281244277954},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.33200642466545105},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30359166860580444},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.1296006441116333},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.055301547050476074},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.052026182413101196}],"concepts":[{"id":"https://openalex.org/C117354338","wikidata":"https://www.wikidata.org/wiki/Q1165112","display_name":"Singleton","level":3,"score":0.8365156650543213},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.7643488645553589},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6164684891700745},{"id":"https://openalex.org/C95925971","wikidata":"https://www.wikidata.org/wiki/Q3100414","display_name":"Parity-check matrix","level":4,"score":0.58788001537323},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5724128484725952},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5610584020614624},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.5461626052856445},{"id":"https://openalex.org/C2779808786","wikidata":"https://www.wikidata.org/wiki/Q6664603","display_name":"Locality","level":2,"score":0.5335807204246521},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.531654417514801},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47253111004829407},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3419281244277954},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.33200642466545105},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30359166860580444},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.1296006441116333},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.055301547050476074},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.052026182413101196},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C2779234561","wikidata":"https://www.wikidata.org/wiki/Q11995","display_name":"Pregnancy","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2017.8006512","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2017.8006512","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1530125006","https://openalex.org/W1902314736","https://openalex.org/W1993830711","https://openalex.org/W1997044393","https://openalex.org/W2022619326","https://openalex.org/W2050413942","https://openalex.org/W2065465262","https://openalex.org/W2510019121","https://openalex.org/W2962735098","https://openalex.org/W2963963730","https://openalex.org/W3083398082","https://openalex.org/W3100004208","https://openalex.org/W4206775542"],"related_works":["https://openalex.org/W2537963609","https://openalex.org/W2092857423","https://openalex.org/W2361792238","https://openalex.org/W2182725540","https://openalex.org/W3126598192","https://openalex.org/W2122913048","https://openalex.org/W2954849755","https://openalex.org/W2066141615","https://openalex.org/W2796395817","https://openalex.org/W2090897912"],"abstract_inverted_index":{"In":[0,55],"an":[1,30],"[n,":[2],"k,":[3,32],"d]":[4],"linear":[5],"code,":[6],"a":[7,69],"code":[8,27,36],"symbol":[9],"is":[10,74],"said":[11],"to":[12],"have":[13],"locality":[14],"r":[15,25],"if":[16],"it":[17],"can":[18],"be":[19,113],"repaired":[20],"by":[21,67],"accessing":[22],"at":[23],"most":[24],"other":[26],"symbols.":[28],"For":[29],"(n,":[31],"r)":[33],"locally":[34],"repairable":[35],"(LRC),":[37],"the":[38,42,108],"minimum":[39,109],"distance":[40,110],"satisfies":[41],"well-known":[43],"Singleton-like":[44,65],"bound":[45,66],"d":[46],"\u2264":[47],"n":[48],"-":[49,51],"k":[50],"[k/r]":[52],"+":[53],"2.":[54],"this":[56,64],"paper,":[57],"we":[58,92],"study":[59],"optimal":[60,87,97],"ternary":[61,88,98],"LRCs":[62,89,99],"meeting":[63],"employing":[68],"parity-check":[70],"matrix":[71],"approach.":[72],"It":[73],"proved":[75],"that":[76],"there":[77],"are":[78],"only":[79,112],"8":[80,103],"classes":[81,104],"of":[82,96,105],"possible":[83],"parameters":[84],"with":[85],"which":[86],"exist.":[90],"Moreover,":[91],"obtain":[93],"explicit":[94],"constructions":[95],"for":[100],"all":[101],"these":[102],"parameters,":[106],"where":[107],"could":[111],"2,":[114],"3,":[115],"4,":[116],"5":[117],"and":[118],"6.":[119]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2}],"updated_date":"2026-04-07T14:57:38.498316","created_date":"2025-10-10T00:00:00"}