{"id":"https://openalex.org/W7114783348","doi":"https://doi.org/10.48550/arxiv.2512.08017","title":"Structure Theorems (and Fast Algorithms) for List Recovery of Subspace-Design Codes","display_name":"Structure Theorems (and Fast Algorithms) for List Recovery of Subspace-Design Codes","publication_year":2025,"publication_date":"2025-12-08","ids":{"openalex":"https://openalex.org/W7114783348","doi":"https://doi.org/10.48550/arxiv.2512.08017"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2512.08017","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.08017","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2512.08017","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Goyal, Rohan","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Goyal, Rohan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Guruswami, Venkatesan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guruswami, Venkatesan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"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/T11130","display_name":"Coding theory and cryptography","score":0.667900025844574,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.667900025844574,"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/T11181","display_name":"Advanced Data Storage Technologies","score":0.25369998812675476,"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":0.016499999910593033,"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/coding-theory","display_name":"Coding theory","score":0.4959000051021576},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.4361000061035156},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.37770000100135803},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.37369999289512634},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.3653999865055084},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.34700000286102295},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.3352000117301941},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.3303000032901764}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5349000096321106},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5037000179290771},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.4959000051021576},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.4361000061035156},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.415800005197525},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3898000121116638},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.37770000100135803},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.37369999289512634},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.3653999865055084},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.34700000286102295},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33820000290870667},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3352000117301941},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3303000032901764},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.32679998874664307},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.31529998779296875},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.31450000405311584},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.3003999888896942},{"id":"https://openalex.org/C2776085556","wikidata":"https://www.wikidata.org/wiki/Q183361","display_name":"Chen","level":2,"score":0.2818000018596649},{"id":"https://openalex.org/C43126263","wikidata":"https://www.wikidata.org/wiki/Q128751","display_name":"Source code","level":2,"score":0.27630001306533813},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.26460000872612},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.258899986743927},{"id":"https://openalex.org/C39635130","wikidata":"https://www.wikidata.org/wiki/Q7226636","display_name":"Polynomial code","level":5,"score":0.2540999948978424},{"id":"https://openalex.org/C42276685","wikidata":"https://www.wikidata.org/wiki/Q795705","display_name":"BCH code","level":3,"score":0.2533000111579895},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.25279998779296875}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2512.08017","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.08017","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":"doi:10.48550/arxiv.2512.08017","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.08017","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"List":[0],"recovery":[1],"of":[2,42,106,122,138,141,184],"error-correcting":[3],"codes":[4,27,62,65,87],"has":[5],"emerged":[6],"as":[7],"a":[8,40,135,139],"fundamental":[9],"notion":[10],"with":[11],"broad":[12],"applications":[13],"across":[14],"coding":[15],"theory":[16],"and":[17,24,53,55,63,109,167],"theoretical":[18],"computer":[19],"science.":[20],"Folded":[21],"Reed-Solomon":[22,61],"(FRS)":[23],"univariate":[25],"multiplicity":[26],"are":[28,124,127],"explicit":[29],"constructions":[30],"which":[31,146],"can":[32,133],"be":[33],"efficiently":[34],"list-recovered":[35],"up":[36],"to":[37,98,165],"capacity,":[38],"namely":[39],"fraction":[41],"errors":[43],"approaching":[44],"$1-R$":[45],"where":[46],"$R$":[47],"is":[48,91],"the":[49,117,120,148,177,182],"code":[50],"rate.":[51],"Chen":[52],"Zhang":[54],"related":[56],"works":[57],"showed":[58],"that":[59,82,90,114],"folded":[60],"linear":[64],"must":[66],"have":[67],"list":[68,112],"sizes":[69],"exponential":[70],"in":[71,88,94,119,153,157],"$1/\u03b5$":[72,158],"for":[73,111,181],"list-recovering":[74],"from":[75],"an":[76],"error-fraction":[77],"$1-R-\u03b5$.":[78],"These":[79],"results":[80,180],"suggest":[81],"one":[83],"cannot":[84],"list-recover":[85],"FRS":[86],"time":[89,154],"also":[92,174],"polynomial":[93,156],"$1/\u03b5$.":[95],"In":[96,130],"contrast":[97],"such":[99],"limitations,":[100],"we":[101,132],"show,":[102],"extending":[103],"algorithmic":[104,179],"advances":[105],"Ashvinkumar,":[107],"Habib,":[108],"Srivastava":[110],"decoding,":[113],"even":[115],"if":[116],"lists":[118],"case":[121],"list-recovery":[123],"large,":[125],"they":[126],"highly":[128],"structured.":[129],"particular,":[131],"output":[134],"compact":[136,162],"description":[137,163],"set":[140],"size":[142,170],"only":[143,155],"$\\ell^{O((\\log":[144],"\\ell)/\u03b5)}$":[145],"contains":[147],"relevant":[149],"list,":[150],"while":[151],"running":[152],"(the":[159],"previously":[160],"known":[161],"due":[164],"Guruswami":[166],"Wang":[168],"had":[169],"$\\approx":[171],"n^{\\ell/\u03b5}$).":[172],"We":[173],"improve":[175],"on":[176],"state-of-the-art":[178],"task":[183],"list-recovery.":[185]},"counts_by_year":[],"updated_date":"2025-12-11T23:13:37.075516","created_date":"2025-12-11T00:00:00"}
