{"id":"https://openalex.org/W7166061561","doi":"https://doi.org/10.48550/arxiv.2606.26742","title":"Tight Lower Bounds and Optimal Constructions of Locally Repairable Convertible Codes in the Split Regime","display_name":"Tight Lower Bounds and Optimal Constructions of Locally Repairable Convertible Codes in the Split Regime","publication_year":2026,"publication_date":"2026-06-25","ids":{"openalex":"https://openalex.org/W7166061561","doi":"https://doi.org/10.48550/arxiv.2606.26742"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.26742","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.26742","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.26742","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110684088","display_name":"Haoming Shi","orcid":"https://orcid.org/0000-0002-4711-6292"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shi, Haoming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5139415615","display_name":"Weijun Fang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fang, Weijun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11181","display_name":"Advanced Data Storage Technologies","score":0.9968000054359436,"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":0.9968000054359436,"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.001500000013038516,"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/T11614","display_name":"Cloud Data Security Solutions","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/erasure-code","display_name":"Erasure code","score":0.5228999853134155},{"id":"https://openalex.org/keywords/distributed-data-store","display_name":"Distributed data store","score":0.4900999963283539},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.48649999499320984},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.476500004529953},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.42829999327659607},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4203000068664551},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.362199991941452},{"id":"https://openalex.org/keywords/erasure","display_name":"Erasure","score":0.3215999901294708}],"concepts":[{"id":"https://openalex.org/C137529215","wikidata":"https://www.wikidata.org/wiki/Q5385031","display_name":"Erasure code","level":3,"score":0.5228999853134155},{"id":"https://openalex.org/C24885549","wikidata":"https://www.wikidata.org/wiki/Q339678","display_name":"Distributed data store","level":2,"score":0.4900999963283539},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.48649999499320984},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.476500004529953},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.42829999327659607},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4275999963283539},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4203000068664551},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4189000129699707},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39160001277923584},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.362199991941452},{"id":"https://openalex.org/C2778790127","wikidata":"https://www.wikidata.org/wiki/Q484885","display_name":"Erasure","level":2,"score":0.3215999901294708},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.31520000100135803},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.31040000915527344},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.31029999256134033},{"id":"https://openalex.org/C103093684","wikidata":"https://www.wikidata.org/wiki/Q7094069","display_name":"Online codes","level":5,"score":0.29190000891685486},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C194739806","wikidata":"https://www.wikidata.org/wiki/Q66221","display_name":"Computer data storage","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.2759000062942505},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2621999979019165},{"id":"https://openalex.org/C2776116443","wikidata":"https://www.wikidata.org/wiki/Q55989","display_name":"Convertible","level":2,"score":0.2581000030040741}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.26742","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.26742","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.26742","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.26742","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Erasure":[0],"codes":[1,63,91,142,158,172],"are":[2,53,64],"a":[3,59],"key":[4],"technique":[5],"for":[6,136],"achieving":[7],"fault-tolerant":[8],"storage":[9,13,16,31],"in":[10,30,98],"modern":[11],"distributed":[12],"systems.":[14],"As":[15],"systems":[17],"evolve,":[18],"their":[19],"code":[20,44,52],"parameters":[21],"often":[22],"need":[23],"to":[24,27,66,178],"be":[25],"adjusted":[26],"accommodate":[28],"changes":[29],"scale,":[32],"reliability":[33],"requirements,":[34],"and":[35,116,156,184,196],"disk":[36],"failure":[37],"rates.":[38],"Such":[39],"adaptation":[40],"is":[41,188],"performed":[42],"through":[43],"conversion,":[45],"where":[46,111],"data":[47,56],"encoded":[48,57],"under":[49,58],"an":[50,145],"initial":[51,115,155],"transformed":[54],"into":[55,190],"final":[60,117,157],"code.":[61],"Convertible":[62],"designed":[65],"carry":[67],"out":[68],"this":[69,81,128],"transformation":[70],"efficiently":[71],"while":[72],"preserving":[73],"desirable":[74],"properties":[75],"of":[76,114,182],"the":[77,95,99,106,112,124,154,161,179,186,191],"underlying":[78],"codes.":[79],"In":[80],"work,":[82],"we":[83,131],"study":[84],"conversions":[85],"between":[86],"systematic":[87],"optimal-distance":[88,138],"locally":[89,139],"repairable":[90,140],"(LRCs),":[92],"focusing":[93],"on":[94,105,153,160,169],"read-bandwidth":[96,133],"cost":[97],"global":[100,118],"split":[101],"regime.":[102],"We":[103,164],"concentrate":[104],"parameter":[107],"range":[108],"\\(g^I,g^F\\le":[109],"r\\),":[110],"numbers":[113],"parity":[119],"nodes":[120],"do":[121],"not":[122],"exceed":[123],"local":[125],"dimension.":[126],"For":[127],"entire":[129],"range,":[130],"derive":[132],"lower":[134],"bounds":[135],"stable":[137],"convertible":[141],"(LRCCs)":[143],"via":[144],"information-theoretic":[146],"approach,":[147],"without":[148],"imposing":[149],"any":[150],"linearity":[151],"assumption":[152],"or":[159],"conversion":[162],"procedure.":[163],"then":[165],"develop":[166],"constructions":[167],"based":[168],"MDS":[170],"array":[171],"with":[173],"prescribed":[174],"repair":[175],"properties.":[176],"According":[177],"relative":[180],"sizes":[181],"\\(g^I\\)":[183],"\\(g^F\\),":[185],"construction":[187],"divided":[189],"three":[192],"cases":[193],"\\(g^F=g^I\\),":[194],"\\(g^F>g^I\\),":[195],"\\(g^F":[197]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-27T00:00:00"}