{"id":"https://openalex.org/W1998698985","doi":"https://doi.org/10.1145/1326554.1326555","title":"Towards 3-query locally decodable codes of subexponential length","display_name":"Towards 3-query locally decodable codes of subexponential length","publication_year":2008,"publication_date":"2008-02-01","ids":{"openalex":"https://openalex.org/W1998698985","doi":"https://doi.org/10.1145/1326554.1326555","mag":"1998698985"},"language":"en","primary_location":{"id":"doi:10.1145/1326554.1326555","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1326554.1326555","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","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/A5046685409","display_name":"Sergey Yekhanin","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]},{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sergey Yekhanin","raw_affiliation_strings":["MIT, Cambridge, Massachusetts","MIT, Cambridge, Massachusetts#TAB#"],"affiliations":[{"raw_affiliation_string":"MIT, Cambridge, Massachusetts","institution_ids":["https://openalex.org/I4210110987"]},{"raw_affiliation_string":"MIT, Cambridge, Massachusetts#TAB#","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046685409"],"corresponding_institution_ids":["https://openalex.org/I4210110987","https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":68.6307,"has_fulltext":false,"cited_by_count":449,"citation_normalized_percentile":{"value":0.99936893,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"55","issue":"1","first_page":"1","last_page":"16"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9998999834060669,"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/T10237","display_name":"Cryptography and Data Security","score":0.9998999834060669,"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/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9970999956130981,"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/mersenne-prime","display_name":"Mersenne prime","score":0.83348548412323},{"id":"https://openalex.org/keywords/code-word","display_name":"Code word","score":0.7558274269104004},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7297231554985046},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5970780253410339},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5497688055038452},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5091068148612976},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4797957241535187},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4242316782474518},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.41426071524620056},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3947082757949829},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22598707675933838},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16351324319839478},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.11485615372657776},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.08305954933166504}],"concepts":[{"id":"https://openalex.org/C29641680","wikidata":"https://www.wikidata.org/wiki/Q186875","display_name":"Mersenne prime","level":2,"score":0.83348548412323},{"id":"https://openalex.org/C153207627","wikidata":"https://www.wikidata.org/wiki/Q863873","display_name":"Code word","level":3,"score":0.7558274269104004},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7297231554985046},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5970780253410339},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5497688055038452},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5091068148612976},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4797957241535187},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4242316782474518},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.41426071524620056},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3947082757949829},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22598707675933838},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16351324319839478},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.11485615372657776},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.08305954933166504},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/1326554.1326555","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1326554.1326555","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.601.9734","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.601.9734","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.di.ens.fr/~vergnaud/algo0910/Locally.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.83.3680","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.3680","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://kam.mff.cuni.cz/~matousek/cla/yekhanin-locallydecodable.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W171567834","https://openalex.org/W182224116","https://openalex.org/W1505096007","https://openalex.org/W1535843738","https://openalex.org/W1540650264","https://openalex.org/W1555149635","https://openalex.org/W1583038314","https://openalex.org/W1832668820","https://openalex.org/W1967703498","https://openalex.org/W1985771908","https://openalex.org/W2000211775","https://openalex.org/W2007208840","https://openalex.org/W2029859729","https://openalex.org/W2048659729","https://openalex.org/W2053086236","https://openalex.org/W2059123783","https://openalex.org/W2064917502","https://openalex.org/W2087207261","https://openalex.org/W2107342895","https://openalex.org/W2120217745","https://openalex.org/W2120282110","https://openalex.org/W2142120204","https://openalex.org/W2150307013","https://openalex.org/W2561675875","https://openalex.org/W3049068437","https://openalex.org/W3103511209","https://openalex.org/W3119119221","https://openalex.org/W3151140615","https://openalex.org/W4230909286","https://openalex.org/W6606458101","https://openalex.org/W6606989391"],"related_works":["https://openalex.org/W2333148107","https://openalex.org/W2536201551","https://openalex.org/W2568469979","https://openalex.org/W1529715114","https://openalex.org/W1978042415","https://openalex.org/W3038654277","https://openalex.org/W2740334431","https://openalex.org/W4212808623","https://openalex.org/W2064466727","https://openalex.org/W1998698985"],"abstract_inverted_index":{"A":[0],"q":[1,38],"-query":[2],"Locally":[3],"Decodable":[4],"Code":[5],"(LDC)":[6],"encodes":[7],"an":[8,14,210,304],"n":[9,98,104,124,134,169,173,179,203,211,224,244,248,254],"-bit":[10,16,212],"message":[11,34],"x":[12,20,30,45],"as":[13],"N":[15,93,166],"codeword":[17,42,53],"C":[18,43],"(":[19,44,97,123,133,202,223],"),":[21,46],"such":[22],"that":[23,71,146,229],"one":[24],"can":[25],"probabilistically":[26],"recover":[27],"any":[28,77],"bit":[29],"i":[31],"of":[32,40,52,62,66,72,91,118,164,200,241,258,268,288],"the":[33,41,108,138,216,266],"by":[35,283],"querying":[36],"only":[37],"bits":[39,54],"even":[47],"after":[48],"some":[49],"constant":[50],"fraction":[51],"has":[55,142],"been":[56,144],"corrupted.":[57],"We":[58,181,192],"give":[59,193],"new":[60],"constructions":[61,157,276],"three":[63,88,159],"query":[64,89,160],"LDCs":[65,90,259],"vastly":[67],"shorter":[68],"length":[69,92,117,165],"than":[70,120],"previous":[73,139,217],"constructions.":[74,140],"Specifically,":[75],"given":[76],"Mersenne":[78,111,151,234],"prime":[79],"p":[80],"=":[81,94,167],"2":[82],"t":[83,100],"\u2212":[84,126,205],"1,":[85],"we":[86,236],"design":[87],"exp(":[95,121,131,168],"O":[96,122,132,170,201,222,245],"1/":[99],")),":[101],"for":[102,176,186,251],"every":[103],".":[105,180,255],"Based":[106],"on":[107,265],"largest":[109],"known":[110],"prime,":[112],"this":[113,154],"translates":[114],"to":[115,130,208,215,301],"a":[116,285,291],"less":[119],"10":[125,204],"7":[127,206],"))":[128,136],"compared":[129,214],"1/2":[135],"in":[137,290,303],"It":[141],"often":[143],"conjectured":[145],"there":[147,230],"are":[148,231,277,281,299],"infinitely":[149,177,232,252],"many":[150,178,233,253],"primes.":[152],"Under":[153],"conjecture,":[155],"our":[156],"yield":[158],"locally":[161],"decodable":[162],"codes":[163],"(1/log":[171,246],"log":[172,247],")":[174,175,207,249,250],"also":[182],"obtain":[183],"analogous":[184],"improvements":[185],"Private":[187],"Information":[188],"Retrieval":[189],"(PIR)":[190],"schemes.":[191],"3-server":[194,238],"PIR":[195,239,261],"schemes":[196,240,262],"with":[197,220],"communication":[198,242],"complexity":[199,221,243],"access":[209],"database,":[213],"best":[218],"scheme":[219],"1/5.25":[225],").":[226],"Assuming":[227],"again":[228],"primes,":[235],"get":[237],"Previous":[256],"families":[257],"and":[260,280],"were":[263],"based":[264],"properties":[267],"low-degree":[269],"multivariate":[270],"polynomials":[271],"over":[272],"finite":[273],"fields.":[274],"Our":[275],"completely":[278],"different":[279],"obtained":[282],"constructing":[284],"large":[286],"number":[287],"vectors":[289],"small":[292],"dimensional":[293],"vector":[294],"space":[295],"whose":[296],"inner":[297],"products":[298],"restricted":[300],"lie":[302],"algebraically":[305],"nice":[306],"set.":[307]},"counts_by_year":[{"year":2025,"cited_by_count":19},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":27},{"year":2020,"cited_by_count":20},{"year":2019,"cited_by_count":29},{"year":2018,"cited_by_count":18},{"year":2017,"cited_by_count":27},{"year":2016,"cited_by_count":23},{"year":2015,"cited_by_count":18},{"year":2014,"cited_by_count":26},{"year":2013,"cited_by_count":43},{"year":2012,"cited_by_count":44}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}