{"id":"https://openalex.org/W2786800728","doi":"https://doi.org/10.4086/toc.2017.v013a011","title":"","display_name":"","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2786800728","doi":"https://doi.org/10.4086/toc.2017.v013a011","mag":"2786800728"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2017.v013a011","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2017.v013a011","pdf_url":"http://www.theoryofcomputing.org/articles/v013a011/v013a011.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://www.theoryofcomputing.org/articles/v013a011/v013a011.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013053155","display_name":"Zeev Dvir","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zeev Dvir","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020540233","display_name":"Shubhangi Saraf","orcid":"https://orcid.org/0009-0005-0874-2978"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shubhangi Saraf","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039043184","display_name":"Avi Wigderson","orcid":"https://orcid.org/0000-0002-1539-1417"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Avi Wigderson","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013053155"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4385,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.70352387,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"13","issue":"1","first_page":"1","last_page":"36"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9983999729156494,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9983999729156494,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9952999949455261,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/combinatorics","display_name":"Combinatorics","score":0.7506250143051147},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6759114265441895},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6074551343917847},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5141677856445312},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.509255051612854},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.460889995098114},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.4524199366569519},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10299408435821533}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7506250143051147},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6759114265441895},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6074551343917847},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5141677856445312},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.509255051612854},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.460889995098114},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.4524199366569519},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10299408435821533},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2017.v013a011","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2017.v013a011","pdf_url":"http://www.theoryofcomputing.org/articles/v013a011/v013a011.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4086/toc.2017.v013a011","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2017.v013a011","pdf_url":"http://www.theoryofcomputing.org/articles/v013a011/v013a011.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1171700966","display_name":null,"funder_award_id":"NSF CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1943969787","display_name":null,"funder_award_id":"CCF-1412958","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3089858946","display_name":null,"funder_award_id":"CCF-1523816","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3396274902","display_name":null,"funder_award_id":"CCF-1350572","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7156878700","display_name":"CAREER: New Directions in Arithmetic Computation","funder_award_id":"1350572","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8047500120","display_name":"AF:  Small:  New Techniques for Private Information Retrieval and Locally Decodable Codes","funder_award_id":"1523816","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8513554395","display_name":null,"funder_award_id":"1451191","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G882115978","display_name":"AF: Large: Theory of Computation - Pushing the State-of-the-Art","funder_award_id":"1412958","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G966786367","display_name":null,"funder_award_id":"DMS-1451191","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2786800728.pdf","grobid_xml":"https://content.openalex.org/works/W2786800728.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W182224116","https://openalex.org/W1481582196","https://openalex.org/W1530008367","https://openalex.org/W1594962164","https://openalex.org/W1965633735","https://openalex.org/W1967703498","https://openalex.org/W1991584875","https://openalex.org/W1996839061","https://openalex.org/W1998698985","https://openalex.org/W2018925011","https://openalex.org/W2019578639","https://openalex.org/W2024011363","https://openalex.org/W2027317757","https://openalex.org/W2037726123","https://openalex.org/W2073346043","https://openalex.org/W2082647621","https://openalex.org/W2120217745","https://openalex.org/W2126216220","https://openalex.org/W2129530428","https://openalex.org/W2132463883","https://openalex.org/W2144581009","https://openalex.org/W2145012723","https://openalex.org/W2148352980","https://openalex.org/W2177108502","https://openalex.org/W2282998501","https://openalex.org/W2293988196","https://openalex.org/W2611959999","https://openalex.org/W2998808137","https://openalex.org/W3004537778","https://openalex.org/W3102478671","https://openalex.org/W4206454995","https://openalex.org/W4226347946","https://openalex.org/W4230909286","https://openalex.org/W4256317935"],"related_works":["https://openalex.org/W2391321755","https://openalex.org/W2896134808","https://openalex.org/W3103861421","https://openalex.org/W1971174658","https://openalex.org/W4211228991","https://openalex.org/W2949110394","https://openalex.org/W2353790329","https://openalex.org/W2279743781","https://openalex.org/W140666874","https://openalex.org/W1553466895"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2,30,39,57,79],"3-query":[3],"linear":[4,46],"locally":[5,97],"correctable":[6,98],"codes":[7,101],"of":[8,48,51,96],"dimension":[9],"d":[10,19,36,60],"over":[11,108],"the":[12,65,73,80],"reals":[13],"require":[14],"block":[15],"length":[16],"n":[17,32,58],">":[18,25,59],"2+":[20,61],"for":[21,90],"some":[22],"fixed,":[23],"positive":[24],"0.":[26],"Geometrically,":[27],"this":[28,85],"means":[29],"if":[31],"vectors":[33],"in":[34,84],"R":[35],"are":[37],"such":[38],"each":[40],"vector":[41],"is":[42,75],"spanned":[43],"by":[44],"a":[45],"number":[47],"disjoint":[49],"triples":[50],"others,":[52],"then":[53],"it":[54],"must":[55],"be":[56,88],".":[62],"This":[63],"improves":[64],"known":[66],"quadratic":[67],"lower":[68,94],"bounds":[69,95],"(e.":[70],"g.,":[71],"While":[72],"improvement":[74],"modest,":[76],"we":[77],"expect":[78],"new":[81],"techniques":[82],"introduced":[83],"article":[86],"will":[87],"useful":[89],"further":[91],"progress":[92],"on":[93],"and":[99],"decodable":[100],"with":[102],"more":[103],"than":[104],"2":[105],"queries,":[106],"possibly":[107],"other":[109],"fields":[110],"as":[111],"well.":[112]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2018-02-23T00:00:00"}
