{"id":"https://openalex.org/W2027857542","doi":"https://doi.org/10.1145/1250790.1250830","title":"Towards 3-query locally decodable codes of subexponential length","display_name":"Towards 3-query locally decodable codes of subexponential length","publication_year":2007,"publication_date":"2007-06-11","ids":{"openalex":"https://openalex.org/W2027857542","doi":"https://doi.org/10.1145/1250790.1250830","mag":"2027857542"},"language":"en","primary_location":{"id":"doi:10.1145/1250790.1250830","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1250790.1250830","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-ninth annual ACM symposium on Theory of computing","raw_type":"proceedings-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, MA","MIT, Cambridge, Ma.#TAB#"],"affiliations":[{"raw_affiliation_string":"MIT, Cambridge, MA","institution_ids":["https://openalex.org/I4210110987"]},{"raw_affiliation_string":"MIT, Cambridge, Ma.#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":11.7336,"has_fulltext":false,"cited_by_count":75,"citation_normalized_percentile":{"value":0.98417556,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"266","last_page":"274"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9977999925613403,"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/code-word","display_name":"Code word","score":0.8502416610717773},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6827511787414551},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6521843075752258},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6005963087081909},{"id":"https://openalex.org/keywords/mersenne-prime","display_name":"Mersenne prime","score":0.5760517716407776},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5734568238258362},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4795498549938202},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4778689742088318},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3723387122154236},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22020208835601807},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19331833720207214},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.14329513907432556},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.06947499513626099}],"concepts":[{"id":"https://openalex.org/C153207627","wikidata":"https://www.wikidata.org/wiki/Q863873","display_name":"Code word","level":3,"score":0.8502416610717773},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6827511787414551},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6521843075752258},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6005963087081909},{"id":"https://openalex.org/C29641680","wikidata":"https://www.wikidata.org/wiki/Q186875","display_name":"Mersenne prime","level":2,"score":0.5760517716407776},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5734568238258362},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4795498549938202},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4778689742088318},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3723387122154236},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22020208835601807},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19331833720207214},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.14329513907432556},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.06947499513626099},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1250790.1250830","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1250790.1250830","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-ninth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W171567834","https://openalex.org/W182224116","https://openalex.org/W274479492","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/W2120282110","https://openalex.org/W2132937716","https://openalex.org/W2142120204","https://openalex.org/W2150307013","https://openalex.org/W2150884088","https://openalex.org/W2608876994","https://openalex.org/W2613956024","https://openalex.org/W3030909269","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","https://openalex.org/W6669064135","https://openalex.org/W6675779156","https://openalex.org/W6782226990"],"related_works":["https://openalex.org/W2363280288","https://openalex.org/W2356863210","https://openalex.org/W2025877929","https://openalex.org/W2382359992","https://openalex.org/W2942776097","https://openalex.org/W2363807867","https://openalex.org/W2952749808","https://openalex.org/W1540650264","https://openalex.org/W2750064252","https://openalex.org/W2119049526"],"abstract_inverted_index":{"A":[0],"q-query":[1],"Locally":[2],"Decodable":[3],"Code":[4],"(LDC)":[5],"encodes":[6],"an":[7,11],"n-bitmessage":[8],"x":[9],"as":[10],"n-bit":[12],"codeword":[13,32,39],"C(x),":[14,33],"such":[15],"that":[16,55,105],"one":[17],"canprobabilistically":[18],"recover":[19],"any":[20],"bit":[21],"xi":[22],"of":[23,30,38,47,51,56,73,90,121],"the":[24,31,98],"message":[25],"by":[26],"queryingonly":[27],"q":[28],"bits":[29,40],"even":[34],"after":[35],"some":[36],"constantfraction":[37],"has":[41],"been":[42,103],"corrupted.We":[43],"give":[44],"new":[45],"constructions":[46,115],"three":[48,70,117],"query":[49,71],"LDCs":[50,72],"vastly":[52],"shorterlength":[53],"than":[54,92],"previous":[57,99],"constructions.":[58,100],"Specifically,":[59],"givenany":[60],"Mersenne":[61,83],"prime":[62],"p":[63],"=":[64],"2t":[65],"-":[66],"1,":[67],"we":[68],"design":[69],"length":[74,89,122],"N=(n1/t),":[75],"for":[76],"every":[77],"n.":[78,128],"Based":[79],"on":[80],"thelargest":[81],"known":[82],"prime,":[84],"this":[85,112],"translates":[86],"to":[87,95],"a":[88],"less":[91],"exp(n10-7),":[93],"compared":[94],"exp(n1/2)":[96],"in":[97],"It":[101],"hasoften":[102],"conjectured":[104],"there":[106],"are":[107],"infinitely":[108],"many":[109,127],"Mersenneprimes.":[110],"Under":[111],"conjecture,":[113],"our":[114],"yield":[116],"querylocally":[118],"decodable":[119],"codes":[120],"N=exp(nO(1/(log":[123],"log":[124],"n)))":[125],"forinfinitely":[126]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
