{"id":"https://openalex.org/W2405116759","doi":"https://doi.org/10.1109/isit.2016.7541566","title":"Bounds on the maximal minimum distance of linear locally repairable codes","display_name":"Bounds on the maximal minimum distance of linear locally repairable codes","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2405116759","doi":"https://doi.org/10.1109/isit.2016.7541566","mag":"2405116759"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2016.7541566","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2016.7541566","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1602.04482","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082039211","display_name":"Antti P\u00f6ll\u00e4nen","orcid":"https://orcid.org/0000-0002-4814-5757"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Antti P\u00f6ll\u00e4nen","raw_affiliation_strings":["Department of Mathematics and Systems Analysis, Aalto University, P.O.Box 11100, FI-00076 Finland","Dept. of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI-00076, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Systems Analysis, Aalto University, P.O.Box 11100, FI-00076 Finland","institution_ids":["https://openalex.org/I9927081"]},{"raw_affiliation_string":"Dept. of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI-00076, Finland","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077043701","display_name":"Thomas Westerb\u00e4ck","orcid":null},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Thomas Westerb\u00e4ck","raw_affiliation_strings":["Department of Mathematics and Systems Analysis, Aalto University, P.O.Box 11100, FI-00076 Finland","Dept. of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI-00076, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Systems Analysis, Aalto University, P.O.Box 11100, FI-00076 Finland","institution_ids":["https://openalex.org/I9927081"]},{"raw_affiliation_string":"Dept. of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI-00076, Finland","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079294052","display_name":"Ragnar Freij-Hollanti","orcid":"https://orcid.org/0000-0001-8156-2053"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Ragnar Freij-Hollanti","raw_affiliation_strings":["Department of Communications and Networking, Aalto University, P.O.Box 13000, FI-00076, Finland","Department of Communications and Networking, Aalto University, P.O. Box 13000, FI-00076, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Communications and Networking, Aalto University, P.O.Box 13000, FI-00076, Finland","institution_ids":["https://openalex.org/I9927081"]},{"raw_affiliation_string":"Department of Communications and Networking, Aalto University, P.O. Box 13000, FI-00076, Finland","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035260653","display_name":"Camilla Hollanti","orcid":"https://orcid.org/0000-0001-5356-8669"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Camilla Hollanti","raw_affiliation_strings":["Department of Mathematics and Systems Analysis, Aalto University, P.O.Box 11100, FI-00076 Finland","Dept. of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI-00076, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Systems Analysis, Aalto University, P.O.Box 11100, FI-00076 Finland","institution_ids":["https://openalex.org/I9927081"]},{"raw_affiliation_string":"Dept. of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI-00076, Finland","institution_ids":["https://openalex.org/I9927081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5082039211"],"corresponding_institution_ids":["https://openalex.org/I9927081"],"apc_list":null,"apc_paid":null,"fwci":0.3037,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.63030783,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1586","last_page":"1590"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11181","display_name":"Advanced Data Storage Technologies","score":0.9995999932289124,"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":0.9995999932289124,"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/T10237","display_name":"Cryptography and Data Security","score":0.980400025844574,"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.9782999753952026,"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/matroid","display_name":"Matroid","score":0.8043583631515503},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7052454948425293},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6636980772018433},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6349503993988037},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5354549884796143},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4322808086872101},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4261902868747711},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.4118843376636505},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1049671471118927},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.061747968196868896}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.8043583631515503},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7052454948425293},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6636980772018433},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6349503993988037},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5354549884796143},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4322808086872101},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4261902868747711},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.4118843376636505},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1049671471118927},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.061747968196868896},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/isit.2016.7541566","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2016.7541566","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1602.04482","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1602.04482","pdf_url":"https://arxiv.org/pdf/1602.04482","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2405116759","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1602.04482.pdf","pdf_url":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:aaltodoc.aalto.fi:123456789/27399","is_oa":true,"landing_page_url":"https://research.aalto.fi/en/publications/92dcdee0-1240-443c-bd1f-321cea1d5292","pdf_url":null,"source":{"id":"https://openalex.org/S4306401663","display_name":"Aaltodoc (Aalto University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9927081","host_organization_name":"Aalto University","host_organization_lineage":["https://openalex.org/I9927081"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"acceptedVersion"},{"id":"doi:10.48550/arxiv.1602.04482","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1602.04482","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1602.04482","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1602.04482","pdf_url":"https://arxiv.org/pdf/1602.04482","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1520448495","https://openalex.org/W1715633553","https://openalex.org/W1993830711","https://openalex.org/W1995147907","https://openalex.org/W1997044393","https://openalex.org/W2006551665","https://openalex.org/W2008976700","https://openalex.org/W2021662392","https://openalex.org/W2022619326","https://openalex.org/W2048889632","https://openalex.org/W2050500290","https://openalex.org/W2155418912","https://openalex.org/W2216541677","https://openalex.org/W2317423124","https://openalex.org/W2761980362","https://openalex.org/W2963963730"],"related_works":["https://openalex.org/W3003747291","https://openalex.org/W3081202096","https://openalex.org/W2962966916","https://openalex.org/W2592011924","https://openalex.org/W2887865132","https://openalex.org/W2751464272","https://openalex.org/W3049672347","https://openalex.org/W2951356926","https://openalex.org/W3122364685","https://openalex.org/W3080558440","https://openalex.org/W1498820893","https://openalex.org/W3029297920","https://openalex.org/W3161786464","https://openalex.org/W2114067035","https://openalex.org/W2137806147","https://openalex.org/W2981217302","https://openalex.org/W2119821558","https://openalex.org/W2219355838","https://openalex.org/W2116555776","https://openalex.org/W2963978969"],"abstract_inverted_index":{"Locally":[0,152],"repairable":[1,125],"codes":[2,7],"(LRCs)":[3],"are":[4],"error":[5],"correcting":[6],"used":[8,238],"in":[9,74,118,143],"distributed":[10],"data":[11],"storage.":[12],"Besides":[13],"a":[14,34,83,94,160,179],"global":[15],"level,":[16],"they":[17],"enable":[18],"errors":[19],"to":[20,48,228,239],"be":[21,46,229],"corrected":[22],"locally,":[23],"reducing":[24],"the":[25,104,149,165,193,211,232,241],"need":[26],"for":[27,62,202,214,231],"communication":[28],"between":[29,37],"storage":[30],"nodes.":[31],"There":[32],"is":[33,99,226,237],"close":[35],"connection":[36],"almost":[38],"affine":[39],"LRCs":[40,51,64,208],"and":[41,52,106,137,209],"matroid":[42,133],"theory":[43],"which":[44,157,203],"can":[45,188],"utilized":[47],"construct":[49],"good":[50],"derive":[53,240],"bounds":[54,243],"on":[55,103,164],"their":[56],"performance.":[57],"A":[58],"generalized":[59],"Singleton":[60],"bound":[61,98,163,213,225],"linear":[63,109,180,207,245],"with":[65,82,182],"parameters":[66,183,196],"(n;":[67,111,174,184,197,219],"k;":[68,112,175,185,198,220],"d;":[69,113,199],"r;":[70,114,176,186,200,221],"\u03b4)":[71,177,187,201],"was":[72],"given":[73,117],"[N.":[75],"Prakash":[76],"et":[77,121,146],"al.,":[78,122,147],"\u201cOptimal":[79,123],"Linear":[80],"Codes":[81],"Local-Error-Correction":[84],"Property\u201d,":[85],"IEEE":[86,127],"Int.":[87],"Symp.":[88],"Inf.":[89],"Theory].":[90],"In":[91],"this":[92,97,224],"paper,":[93],"LRC":[95,181],"achieving":[96],"called":[100],"perfect.":[101],"Results":[102],"existence":[105,136,242],"nonexistence":[107,138],"of":[108,151,195,234,244],"perfect":[110,206],"\u03b4)-LRCs":[115],"were":[116,140],"[W.":[119],"Song":[120],"locally":[124],"codes\u201d,":[126],"J.":[128],"Sel.":[129],"Areas":[130],"Comm.].":[131],"Using":[132],"theory,":[134],"these":[135],"results":[139],"later":[141],"strengthened":[142],"[T.":[144],"Westerb\u00e4ck":[145],"\u201cOn":[148],"Combinatorics":[150],"Repairable":[153],"Codes\u201d,":[154],"Arxiv:":[155],"1501.00153],":[156],"also":[158],"provided":[159],"general":[161],"lower":[162,212],"maximal":[166],"achievable":[167],"minimum":[168],"distance":[169],"d":[170,215],"<sub":[171,216],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[172,217],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">max</sub>":[173,218],"that":[178,236],"have.":[189],"This":[190],"article":[191],"expands":[192],"class":[194,233],"there":[204],"exist":[205],"improves":[210],"\u03b4).":[222],"Further,":[223],"proved":[227],"optimal":[230],"matroids":[235],"LRCs.":[246]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-29T08:15:47.926485","created_date":"2025-10-10T00:00:00"}