{"id":"https://openalex.org/W7170160194","doi":"https://doi.org/10.48550/arxiv.2607.19576","title":"Bounds and Limitations on Codes Achieving List Recovery Capacity","display_name":"Bounds and Limitations on Codes Achieving List Recovery Capacity","publication_year":2026,"publication_date":"2026-07-21","ids":{"openalex":"https://openalex.org/W7170160194","doi":"https://doi.org/10.48550/arxiv.2607.19576"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.19576","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.19576","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.19576","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028220417","display_name":"Joshua Brakensiek","orcid":"https://orcid.org/0000-0003-4149-7298"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Brakensiek, Joshua","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012499307","display_name":"Yeyuan Chen","orcid":"https://orcid.org/0009-0006-5696-4628"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Yeyuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5143511445","display_name":"Aaron Putterman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Putterman, Aaron","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5143491624","display_name":"Zihan Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Zihan","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":0.76419997215271,"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":0.76419997215271,"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":0.10490000247955322,"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":0.01590000092983246,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/impossibility","display_name":"Impossibility","score":0.6121000051498413},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5278000235557556},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4860999882221222},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4693000018596649},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.45890000462532043},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.3905999958515167},{"id":"https://openalex.org/keywords/singleton","display_name":"Singleton","score":0.366100013256073}],"concepts":[{"id":"https://openalex.org/C2776261394","wikidata":"https://www.wikidata.org/wiki/Q315562","display_name":"Impossibility","level":2,"score":0.6121000051498413},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5278000235557556},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5091000199317932},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4860999882221222},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48260000348091125},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4693000018596649},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4650000035762787},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.45890000462532043},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3905999958515167},{"id":"https://openalex.org/C117354338","wikidata":"https://www.wikidata.org/wiki/Q1165112","display_name":"Singleton","level":3,"score":0.366100013256073},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.357699990272522},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30889999866485596},{"id":"https://openalex.org/C76132124","wikidata":"https://www.wikidata.org/wiki/Q5474786","display_name":"Fountain code","level":5,"score":0.2985999882221222},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.29739999771118164},{"id":"https://openalex.org/C206468330","wikidata":"https://www.wikidata.org/wiki/Q834373","display_name":"Code rate","level":3,"score":0.2912999987602234},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.26910001039505005},{"id":"https://openalex.org/C43126263","wikidata":"https://www.wikidata.org/wiki/Q128751","display_name":"Source code","level":2,"score":0.2653999924659729}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.19576","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.19576","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.19576","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.19576","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"},"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":{"In":[0],"coding":[1],"theory,":[2,82],"list":[3,40],"recoverability":[4,41],"is":[5,69,121,167],"a":[6,17,22,98,124,148,168,198,209,239],"fundamental":[7,169],"concept":[8],"which":[9,73,219],"robustly":[10],"captures":[11,220],"how":[12],"``spread-out''":[13],"codewords":[14,49],"are":[15,45],"in":[16,77,171,201,225],"code.":[18],"More":[19],"formally,":[20],"given":[21],"code":[23,127,236],"$C":[24],"\\subseteq":[25,33],"\u03a3^n$":[26],"and":[27,89,111,146,156,245],"input":[28],"lists":[29],"$S_1,":[30],"\\dots,":[31],"S_n":[32],"\u03a3$":[34],"of":[35,63,140,204,211],"size":[36],"at":[37,46,59],"most":[38,47],"$\\ell$,":[39],"requires":[42],"that":[43,54,106,165,174,233],"there":[44,166],"$L$":[48],"$c":[50],"\\in":[51,56,65],"C$":[52],"such":[53,212,222],"$c_i":[55],"S_i$":[57],"for":[58,107,123,243],"least":[60],"$(1-\u03c1)n$":[61],"choices":[62],"$i":[64],"[n]$.":[66],"List":[67],"recovery":[68],"an":[70,216],"important":[71],"question":[72],"has":[74,185],"found":[75],"applications":[76],"many":[78],"areas,":[79],"including":[80],"complexity":[81],"property":[83],"testing,":[84],"compressed":[85],"sensing,":[86],"streaming":[87],"algorithms,":[88],"cryptography.":[90],"As":[91],"our":[92,141,159],"first":[93],"main":[94,161],"result,":[95,162],"we":[96,104,117,163,231],"establish":[97],"tight":[99],"``generalized":[100],"singleton":[101],"bound''.":[102],"Formally,":[103],"show":[105,232],"constant":[108],"$\\ell,":[109],"L,\u03c1$":[110],"sufficiently":[112],"large":[113],"alphabets":[114],"$\u03a3$,":[115],"if":[116],"define":[118],"$R^*=\\frac{L+1-\\ell}{L}-\\frac{L+1}{L}\u03c1$,":[119],"it":[120],"possible":[122],"$(\u03c1,\\ell,L)$":[125],"list-recoverable":[126,180],"to":[128,134,153,176],"have":[129,135],"rate":[130,136],"$R^*-\u03b5$":[131],"but":[132],"impossible":[133],"$R^*+\u03b5$.":[137],"One":[138],"direction":[139],"result":[142,151],"already":[143],"directly":[144],"generalizes":[145],"improves":[147],"weaker":[149],"impossibility":[150],"due":[152],"Goldberg,":[154],"Shangguan,":[155],"Tamo.":[157],"For":[158],"second":[160],"prove":[164],"shortcoming":[170],"existing":[172],"methods":[173],"aim":[175],"construct":[177],"explicit,":[178],"optimal":[179],"codes.":[181,247],"Indeed,":[182],"recent":[183,223],"work":[184,203],"constructed":[186],"explicit":[187],"codes":[188],"achieving":[189],"list-decoding":[190],"capacity":[191],"(along":[192],"with":[193],"other":[194],"related":[195],"properties)":[196],"using":[197],"framework":[199],"introduced":[200],"the":[202,226],"Alon--Edmonds--Luby":[205],"(AEL).":[206],"We":[207],"give":[208],"meta-analysis":[210],"constructions":[213,224],"by":[214],"presenting":[215],"``AEL":[217],"framework''":[218],"all":[221],"literature.":[227],"Within":[228],"this":[229],"framework,":[230],"no":[234],"AEL-based":[235],"can":[237],"break":[238],"recently-identified":[240],"list-recovery":[241],"barrier":[242],"additive":[244],"linear":[246]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-24T00:00:00"}