{"id":"https://openalex.org/W1554836672","doi":"https://doi.org/10.1145/1374376.1374418","title":"Decodability of group homomorphisms beyond the johnson bound","display_name":"Decodability of group homomorphisms beyond the johnson bound","publication_year":2008,"publication_date":"2008-05-17","ids":{"openalex":"https://openalex.org/W1554836672","doi":"https://doi.org/10.1145/1374376.1374418","mag":"1554836672"},"language":"en","primary_location":{"id":"doi:10.1145/1374376.1374418","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1374376.1374418","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the fortieth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},"type":"conference-paper","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/A5029616850","display_name":"Irit Dinur","orcid":"https://orcid.org/0000-0002-4335-5237"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Irit Dinur","raw_affiliation_strings":["Weizmann Institute of Science, Rehovot, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weizmann Institute of Science, Rehovot, Israel","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090091569","display_name":"Elena Grigorescu","orcid":"https://orcid.org/0000-0001-9673-4313"},"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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Elena Grigorescu","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031695135","display_name":"Swastik Kopparty","orcid":"https://orcid.org/0000-0003-2704-8808"},"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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Swastik Kopparty","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101519422","display_name":"Madhu Sudan","orcid":"https://orcid.org/0000-0003-3718-6489"},"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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Madhu Sudan","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0072,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.73287961,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"15","issue":null,"first_page":"275","last_page":"284"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9983999729156494,"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/T12029","display_name":"DNA and Biological Computing","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.8417965173721313},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.7774515151977539},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6883691549301147},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.5927649140357971},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5871612429618835},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4941916763782501},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4393691122531891},{"id":"https://openalex.org/keywords/lift","display_name":"Lift (data mining)","score":0.4180290400981903},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.37771865725517273},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.19017192721366882},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1495746672153473},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12025377154350281},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.09819459915161133}],"concepts":[{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.8417965173721313},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7774515151977539},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6883691549301147},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.5927649140357971},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5871612429618835},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4941916763782501},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4393691122531891},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.4180290400981903},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.37771865725517273},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.19017192721366882},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1495746672153473},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12025377154350281},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.09819459915161133},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1145/1374376.1374418","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1374376.1374418","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the fortieth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.123.9347","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.123.9347","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://theory.lcs.mit.edu/~madhu/papers/dgks-conf.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.129.6734","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.129.6734","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://theory.lcs.mit.edu/~madhu/papers/dgks-full.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.186.6115","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.186.6115","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.wisdom.weizmann.ac.il/%7Edinuri/mypapers/DGKS08.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.189.3046","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.189.3046","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.mit.edu/elena_g/www/papers/group2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.634.3718","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.634.3718","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eccc.hpi-web.de/report/2008/020/download/","raw_type":"text"},{"id":"mag:1554836672","is_oa":false,"landing_page_url":"http://eccc.hpi-web.de/eccc-reports/2008/TR08-020/index.html","pdf_url":null,"source":{"id":"https://openalex.org/S11189987","display_name":"Electronic colloquium on computational complexity","issn_l":"1433-8092","issn":["1433-8092"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Electronic colloquium on computational complexity","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1554836672","https://openalex.org/W1593724039","https://openalex.org/W1901622511","https://openalex.org/W1996584657","https://openalex.org/W2012365979","https://openalex.org/W2027528470","https://openalex.org/W2063130531","https://openalex.org/W2095546965","https://openalex.org/W2113204179","https://openalex.org/W2133589924","https://openalex.org/W2152263739","https://openalex.org/W2157915592","https://openalex.org/W2293852858","https://openalex.org/W2963148175"],"related_works":["https://openalex.org/W2805450713","https://openalex.org/W2995126662","https://openalex.org/W1587657500","https://openalex.org/W2950426762","https://openalex.org/W1484454814","https://openalex.org/W2051569409","https://openalex.org/W3135887889","https://openalex.org/W3022249633","https://openalex.org/W3197445909","https://openalex.org/W2058435648","https://openalex.org/W2950522257","https://openalex.org/W2950271964","https://openalex.org/W2144581009","https://openalex.org/W2000304127","https://openalex.org/W64198012","https://openalex.org/W3098926890","https://openalex.org/W2222858103","https://openalex.org/W3104769525","https://openalex.org/W1995343556","https://openalex.org/W2794887178"],"abstract_inverted_index":{"Given":[0],"a":[1,49,71,132],"pair":[2,35,79],"of":[3,11,36,51,61,80,90,115,135,145,178,207,233],"finite":[4],"groups":[5,38,82,187,200],"G":[6,14,39,83,97],"and":[7,40,84,107,153,192],"H,":[8,41,85,112],"the":[9,28,42,59,65,87,113,141,151,155,176,183,218,224],"set":[10],"homomorphisms":[12,95,116,197],"from":[13,48,96,196],"to":[15,55,98,162,173,175,213,221],"H":[16,99],"form":[17],"an":[18,171],"error-correcting":[19],"code":[20,44],"where":[21],"codewords":[22],"differ":[23],"in":[24,150],"at":[25,126],"least":[26],"1/2":[27],"coordinates.":[29],"We":[30,129,181,210,227],"show":[31],"that":[32,76,117,157,185],"for":[33,77,103,154,217,223],"every":[34,78,104,108],"abelian":[37,81,186,199],"resulting":[43],"is":[45,64,70,100,125,170],"(locally)":[46],"list-decodable":[47],"fraction":[50,89],"errors":[52],"arbitrarily":[53],"close":[54],"its":[56],"distance.":[57],"At":[58],"heart":[60],"this":[62],"result":[63],"following":[66],"combinatorial":[67],"result:":[68],"There":[69],"fixed":[72],"polynomial":[73],"p(\u2022)":[74],"such":[75,146,179],"if":[86],"maximum":[88],"agreement":[91,119],"between":[92],"two":[93],"distinct":[94],"\u039b,":[101],"then":[102],"\u03b5>":[105],"0":[106],"function":[109],"f:G":[110],"->":[111],"number":[114],"have":[118],"\u039b":[120],"+":[121],"\u03b5":[122],"with":[123],"f":[124],"most":[127],"p(1/\u03b5).":[128],"thus":[130,193],"give":[131,211],"broad":[133],"class":[134],"codes":[136,147,194,220],"whose":[137],"list-decoding":[138,215],"radius":[139],"exceeds":[140],"\"Johnson":[142],"bound\".":[143],"Examples":[144],"are":[148,166],"rare":[149],"literature,":[152],"ones":[156,191],"do":[158],"exist,":[159],"\"combinatorial\"":[160],"techniques":[161,212,230],"analyze":[163],"their":[164],"list-decodability":[165],"limited.":[167],"Our":[168],"work":[169],"attempt":[172],"add":[174],"body":[177],"techniques.":[180],"use":[182],"fact":[184],"decompose":[188],"into":[189],"simpler":[190,208],"derived":[195],"over":[198],"may":[201,231],"be":[202,232],"viewed":[203],"as":[204],"certain":[205],"\"compositions\"":[206],"codes.":[209],"lift":[214],"bounds":[216,222],"component":[219],"composed":[225],"code.":[226],"believe":[228],"these":[229],"general":[234],"interest.":[235]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
