{"id":"https://openalex.org/W4401749287","doi":"https://doi.org/10.1109/tit.2024.3448265","title":"Bounds and Constructions of Singleton-Optimal Locally Repairable Codes With Small Localities","display_name":"Bounds and Constructions of Singleton-Optimal Locally Repairable Codes With Small Localities","publication_year":2024,"publication_date":"2024-08-22","ids":{"openalex":"https://openalex.org/W4401749287","doi":"https://doi.org/10.1109/tit.2024.3448265"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2024.3448265","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2024.3448265","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/A5018855940","display_name":"Weijun Fang","orcid":"https://orcid.org/0000-0003-4121-290X"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]},{"id":"https://openalex.org/I4210132990","display_name":"State Key Laboratory of Cryptology","ror":"https://ror.org/02pn5rj08","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210132990"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weijun Fang","raw_affiliation_strings":["Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Qingdao, China"],"raw_orcid":"https://orcid.org/0000-0003-4121-290X","affiliations":[{"raw_affiliation_string":"Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Qingdao, China","institution_ids":["https://openalex.org/I4210132990","https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100372988","display_name":"Ran Tao","orcid":"https://orcid.org/0000-0003-2064-7429"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]},{"id":"https://openalex.org/I4210132990","display_name":"State Key Laboratory of Cryptology","ror":"https://ror.org/02pn5rj08","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210132990"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ran Tao","raw_affiliation_strings":["Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Qingdao, China"],"raw_orcid":"https://orcid.org/0000-0003-2064-7429","affiliations":[{"raw_affiliation_string":"Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Qingdao, China","institution_ids":["https://openalex.org/I4210132990","https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063946169","display_name":"Fang\u2010Wei Fu","orcid":"https://orcid.org/0000-0002-9696-8977"},"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":"Fang-Wei Fu","raw_affiliation_strings":["Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, China"],"raw_orcid":"https://orcid.org/0000-0002-9696-8977","affiliations":[{"raw_affiliation_string":"Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100427338","display_name":"Bin Chen","orcid":"https://orcid.org/0000-0002-4798-230X"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bin Chen","raw_affiliation_strings":["Department of Computer Science and Technology, Harbin Institute of Technology, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0002-4798-230X","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, Harbin Institute of Technology, Shenzhen, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034104790","display_name":"Shu\u2010Tao Xia","orcid":"https://orcid.org/0000-0002-8639-982X"},"institutions":[{"id":"https://openalex.org/I4210114105","display_name":"Tsinghua\u2013Berkeley Shenzhen Institute","ror":"https://ror.org/02hhwwz98","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210114105","https://openalex.org/I95457486","https://openalex.org/I99065089"]},{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shu-Tao Xia","raw_affiliation_strings":["Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0002-8639-982X","affiliations":[{"raw_affiliation_string":"Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen, China","institution_ids":["https://openalex.org/I4210114105","https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8647,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.76121491,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"70","issue":"10","first_page":"6842","last_page":"6856"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9350000023841858,"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"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9350000023841858,"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/T11181","display_name":"Advanced Data Storage Technologies","score":0.9290000200271606,"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/singleton","display_name":"Singleton","score":0.8035939335823059},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5096051692962646},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38375338912010193},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32508599758148193}],"concepts":[{"id":"https://openalex.org/C117354338","wikidata":"https://www.wikidata.org/wiki/Q1165112","display_name":"Singleton","level":3,"score":0.8035939335823059},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5096051692962646},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38375338912010193},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32508599758148193},{"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/C2779234561","wikidata":"https://www.wikidata.org/wiki/Q11995","display_name":"Pregnancy","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2024.3448265","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2024.3448265","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":[{"display_name":"Sustainable cities and communities","score":0.7200000286102295,"id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G1589626063","display_name":null,"funder_award_id":"ZR2022QA031","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G1677507391","display_name":null,"funder_award_id":"2021YFA1001000","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G2802018518","display_name":null,"funder_award_id":"62171248","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4015711035","display_name":null,"funder_award_id":"61971243","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5117972318","display_name":null,"funder_award_id":"12226336","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5445606270","display_name":null,"funder_award_id":"ZR2022QA069","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G5563798569","display_name":null,"funder_award_id":"12141108","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7511118009","display_name":null,"funder_award_id":"2018YFA0704703","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G8377584638","display_name":null,"funder_award_id":"2022YFA1004900","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G8461867122","display_name":null,"funder_award_id":"62371259","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8545864784","display_name":null,"funder_award_id":"62201322","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8890425352","display_name":null,"funder_award_id":"2022YFA1005000","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null},{"id":"https://openalex.org/F4320329998","display_name":"Nankai Zhide Foundation","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1499271983","https://openalex.org/W1606480398","https://openalex.org/W1993830711","https://openalex.org/W1997044393","https://openalex.org/W2050500290","https://openalex.org/W2124113125","https://openalex.org/W2155418912","https://openalex.org/W2210977112","https://openalex.org/W2510019121","https://openalex.org/W2593205974","https://openalex.org/W2885726234","https://openalex.org/W2944336509","https://openalex.org/W2963503165","https://openalex.org/W2963890921","https://openalex.org/W2963911258","https://openalex.org/W2964317282","https://openalex.org/W2979363856","https://openalex.org/W3010113848","https://openalex.org/W3081202096","https://openalex.org/W3083398082","https://openalex.org/W3095793903","https://openalex.org/W3100004208","https://openalex.org/W3122364685","https://openalex.org/W4225765805","https://openalex.org/W4230314857","https://openalex.org/W4254448470","https://openalex.org/W4284965812","https://openalex.org/W4297977762","https://openalex.org/W4308965115","https://openalex.org/W4312496252","https://openalex.org/W4386025591","https://openalex.org/W6839618655"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W747331120","https://openalex.org/W2351588585","https://openalex.org/W4233660055","https://openalex.org/W2076370897","https://openalex.org/W2906951486","https://openalex.org/W3125437892","https://openalex.org/W2224172171","https://openalex.org/W1965730239"],"abstract_inverted_index":{"An":[0],"<inline-formula":[1,68,86,99,107,114,121,129,143,151,166,190,197,205,241,249,259,268,282,309,320],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[2,69,87,100,108,115,122,130,144,152,167,191,198,206,242,250,260,269,283,310,321],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[3,70,88,101,109,116,123,131,145,153,168,192,199,207,243,251,261,270,284,311,322],"<tex-math":[4,71,89,102,110,117,124,132,146,154,169,193,200,208,244,252,262,271,285,312,323],"notation=\"LaTeX\">$(n,":[5,90,313],"k,":[6,91,314],"d;":[7,92],"r)_{q}$":[8,93],"</tex-math></inline-formula>-locally":[9],"repairable":[10],"code":[11,297],"(LRC)":[12],"is":[13,255],"called":[14],"a":[15,39],"Singleton-optimal":[16,35,60,85,189,236,267],"LRC":[17],"if":[18],"it":[19],"achieves":[20],"the":[21,26,30,56,77,186,232,291,295,306],"Singleton-type":[22],"bound.":[23],"Analogous":[24],"to":[25],"classical":[27],"MDS":[28],"conjecture,":[29],"maximal":[31],"length":[32,57,233,298],"problem":[33],"of":[34,41,58,188,219,234,294,308],"LRCs":[36,61,237,318],"has":[37],"attracted":[38],"lot":[40],"attention":[42],"in":[43,221],"recent":[44],"years.":[45],"In":[46,81],"this":[47],"paper,":[48],"we":[49,95,181,229],"give":[50],"an":[51],"improved":[52],"upper":[53,256],"bound":[54],"for":[55,83,164,196,299,319],"q-ary":[59,235],"with":[62,120,212,225,238,276],"disjoint":[63,213,277],"repair":[64,214,278],"groups":[65,215,279],"such":[66,280],"that":[67,231,281],"notation=\"LaTeX\">$(r+1)\\mid":[72],"n$":[73,287],"</tex-math></inline-formula>":[74,112,119,149,163,203,211,246,254,288],"based":[75],"on":[76],"parity-check":[78],"matrix":[79],"approach.":[80],"particular,":[82],"any":[84,165],"</tex-math></inline-formula>-LRCs,":[94],"show":[96],"that:":[97],"1)":[98],"notation=\"LaTeX\">$n\\le":[103],"q+d-4$":[104],"</tex-math></inline-formula>,":[105,141],"when":[106,142],"notation=\"LaTeX\">$r=2$":[111],"and":[113,150,204,216,247,289],"notation=\"LaTeX\">$d=3e+8$":[118],"notation=\"LaTeX\">$e\\ge":[125],"0$":[126],"</tex-math></inline-formula>;":[127],"2)":[128],"notation=\"LaTeX\">$n\\leq":[133],"(r+1)\\left":[134],"\\lfloor":[135,173],"{{\\frac":[136,174],"{2(q^{2}+q+1)}{r(r+1)}":[137],"+e+1}}\\right":[138],"\\rfloor":[139,177],"$":[140,178],"notation=\"LaTeX\">$d\\ge":[147],"8$":[148],"notation=\"LaTeX\">$\\max":[155],"\\left":[156,172],"\\{{{3,\\frac":[157],"{d-e-6}{e+1}}}\\right":[158],"\\}\\le":[159],"r\\le":[160],"\\frac":[161],"{d-e-3}{e+1}$":[162],"notation=\"LaTeX\">$0\\le":[170],"e\\le":[171],"{d-6}{4}":[175],"}}\\right":[176],"</tex-math></inline-formula>.":[179,264,328],"Furthermore,":[180],"establish":[182],"equivalent":[183],"connections":[184],"between":[185],"existence":[187,307],"notation=\"LaTeX\">$(n,k,d;r)_{q}$":[194],"</tex-math></inline-formula>-LRCs":[195],"notation=\"LaTeX\">$d=6,":[201],"r=3$":[202],"notation=\"LaTeX\">$d=7,":[209],"r=2$":[210],"some":[217,300],"subsets":[218],"lines":[220],"finite":[222],"projective":[223],"space":[224],"certain":[226],"properties.":[227],"Consequently,":[228],"prove":[230,305],"minimum":[239],"distance":[240],"notation=\"LaTeX\">$d=6$":[245],"locality":[248],"notation=\"LaTeX\">$r=3$":[253],"bounded":[257],"by":[258],"notation=\"LaTeX\">$O(q^{1.5})$":[263],"We":[265,303],"construct":[266],"notation=\"LaTeX\">$(8\\le":[272],"n\\le":[273],"q+1,k,d=6,r=3)_{q}$":[274],"</tex-math></inline-formula>-LRC":[275],"notation=\"LaTeX\">$4\\mid":[286],"determine":[290],"exact":[292],"value":[293],"maximum":[296],"specific":[301],"q.":[302],"also":[304],"d=7;":[315],"r=2)_{q}$":[316],"</tex-math></inline-formula>-Singleton-optimal":[317],"notation=\"LaTeX\">$n":[324],"\\approx":[325],"\\sqrt":[326],"{2}q$":[327]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
