{"id":"https://openalex.org/W3100403143","doi":"https://doi.org/10.1109/tit.2021.3131992","title":"Efficient List-Decoding With Constant Alphabet and List Sizes","display_name":"Efficient List-Decoding With Constant Alphabet and List Sizes","publication_year":2021,"publication_date":"2021-06-15","ids":{"openalex":"https://openalex.org/W3100403143","doi":"https://doi.org/10.1109/tit.2021.3131992","mag":"3100403143"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3131992","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3131992","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2011.05884","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004777401","display_name":"Zeyu Guo","orcid":"https://orcid.org/0000-0001-7893-4346"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]},{"id":"https://openalex.org/I91203450","display_name":"University of Haifa","ror":"https://ror.org/02f009v59","country_code":"IL","type":"education","lineage":["https://openalex.org/I91203450"]}],"countries":["IL","US"],"is_corresponding":true,"raw_author_name":"Zeyu Guo","raw_affiliation_strings":["Department of Computer Science, The University of Texas, Austin, TX, USA","Department of Computer Science, University of Haifa, Haifa, Israel","University of Haifa, Israel,"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, The University of Texas, Austin, TX, USA","institution_ids":["https://openalex.org/I86519309"]},{"raw_affiliation_string":"Department of Computer Science, University of Haifa, Haifa, Israel","institution_ids":["https://openalex.org/I91203450"]},{"raw_affiliation_string":"University of Haifa, Israel,","institution_ids":["https://openalex.org/I91203450"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053736571","display_name":"Noga Ron\u2010Zewi","orcid":"https://orcid.org/0000-0002-8416-893X"},"institutions":[{"id":"https://openalex.org/I91203450","display_name":"University of Haifa","ror":"https://ror.org/02f009v59","country_code":"IL","type":"education","lineage":["https://openalex.org/I91203450"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Noga Ron-Zewi","raw_affiliation_strings":["Department of Computer Science, University of Haifa, Haifa, Israel","university of Haifa"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Haifa, Haifa, Israel","institution_ids":["https://openalex.org/I91203450"]},{"raw_affiliation_string":"university of Haifa","institution_ids":["https://openalex.org/I91203450"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004777401"],"corresponding_institution_ids":["https://openalex.org/I86519309","https://openalex.org/I91203450"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0257291,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"68","issue":"3","first_page":"1502","last_page":"1515"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13497","display_name":"Hermeneutics and Narrative Identity","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/1211","display_name":"Philosophy"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T13497","display_name":"Hermeneutics and Narrative Identity","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/1211","display_name":"Philosophy"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13695","display_name":"Aging, Elder Care, and Social Issues","score":0.9749000072479248,"subfield":{"id":"https://openalex.org/subfields/3600","display_name":"General Health Professions"},"field":{"id":"https://openalex.org/fields/36","display_name":"Health Professions"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T13099","display_name":"Health, Medicine and Society","score":0.95660001039505,"subfield":{"id":"https://openalex.org/subfields/3600","display_name":"General Health Professions"},"field":{"id":"https://openalex.org/fields/36","display_name":"Health Professions"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6741376519203186},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.6716005802154541},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5707629323005676},{"id":"https://openalex.org/keywords/affine-space","display_name":"Affine space","score":0.5701415538787842},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5384670495986938},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5215544700622559},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.514602541923523},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.4818200170993805},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4757646918296814},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4706658124923706},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4467686116695404},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.42526373267173767},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.3901765048503876},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.31740373373031616},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.3105446994304657},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18522274494171143},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1580594778060913},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.1198398768901825},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08286973834037781}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6741376519203186},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.6716005802154541},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5707629323005676},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.5701415538787842},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5384670495986938},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5215544700622559},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.514602541923523},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.4818200170993805},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4757646918296814},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4706658124923706},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4467686116695404},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42526373267173767},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.3901765048503876},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.31740373373031616},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.3105446994304657},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18522274494171143},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1580594778060913},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.1198398768901825},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08286973834037781},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2021.3131992","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3131992","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"doi:10.1145/3406325.3451046","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3406325.3451046","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2011.05884","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.05884","pdf_url":"https://arxiv.org/pdf/2011.05884","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2011.05884","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2011.05884","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2011.05884","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.05884","pdf_url":"https://arxiv.org/pdf/2011.05884","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8666992931","display_name":null,"funder_award_id":"735/20","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3100403143.pdf","grobid_xml":"https://content.openalex.org/works/W3100403143.grobid-xml"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W1517959386","https://openalex.org/W1557415002","https://openalex.org/W1593251595","https://openalex.org/W1901622511","https://openalex.org/W1969971421","https://openalex.org/W1996118782","https://openalex.org/W2013369084","https://openalex.org/W2013452229","https://openalex.org/W2027528470","https://openalex.org/W2032431003","https://openalex.org/W2036311506","https://openalex.org/W2052755788","https://openalex.org/W2065853216","https://openalex.org/W2068593329","https://openalex.org/W2089272132","https://openalex.org/W2090418561","https://openalex.org/W2095546965","https://openalex.org/W2100661986","https://openalex.org/W2111393415","https://openalex.org/W2129270830","https://openalex.org/W2131723039","https://openalex.org/W2138036903","https://openalex.org/W2144253890","https://openalex.org/W2146078064","https://openalex.org/W2148352980","https://openalex.org/W2148575324","https://openalex.org/W2150616341","https://openalex.org/W2159193690","https://openalex.org/W2165005000","https://openalex.org/W2168219305","https://openalex.org/W2293852858","https://openalex.org/W2399214554","https://openalex.org/W2625993870","https://openalex.org/W2743386081","https://openalex.org/W2790740792","https://openalex.org/W2962891889","https://openalex.org/W2963309538","https://openalex.org/W2981502670","https://openalex.org/W2982506607","https://openalex.org/W2998808137","https://openalex.org/W3013168409","https://openalex.org/W3085262258","https://openalex.org/W3103427415","https://openalex.org/W3117811306","https://openalex.org/W3128080671","https://openalex.org/W3129091168","https://openalex.org/W4242862564","https://openalex.org/W4245546321","https://openalex.org/W4252614677","https://openalex.org/W6742296631"],"related_works":["https://openalex.org/W28145769","https://openalex.org/W58648772","https://openalex.org/W7297611","https://openalex.org/W9340065","https://openalex.org/W39879777","https://openalex.org/W59127591","https://openalex.org/W279495","https://openalex.org/W48987182","https://openalex.org/W16157872","https://openalex.org/W59564462"],"abstract_inverted_index":{"We":[0,371],"present":[1],"an":[2,46,50,66,311],"explicit":[3,222,385],"and":[4,19,35,148,172,197,223,266,281,327,390,398],"efficient":[5,224],"algebraic":[6,47],"construction":[7,48],"of":[8,49,53,56,68,92,135,226,239,301,314,317,361,369,388],"capacity-achieving":[9,227],"list":[10,21,81,95,128,173,201,228,259,300,330],"decodable":[11,229],"codes":[12,55,111,230,262,273,303],"with":[13,94,274,282,304],"<italic":[14,179,319,323,347,393],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[15,28,37,59,71,86,100,118,140,160,180,184,206,241,320,324,348,394],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">both</i>":[16],"constant":[17,20,338,367],"alphabet":[18,67,257],"sizes.":[22,260],"More":[23],"specifically,":[24],"for":[25,151,193],"any":[26,362],"<inline-formula":[27,36,58,70,85,99,117,139,159,183,205,240],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[29,38,60,72,87,101,119,141,161,185,207,242],"<tex-math":[30,39,61,73,88,102,120,142,162,186,208,243],"notation=\"LaTeX\">$R":[31],"\\in":[32],"(0,1)$":[33],"</tex-math></inline-formula>":[34,42,63,76,90,107,124,146,167,190,217,247],"notation=\"LaTeX\">$\\epsilon":[40],"&gt;0$":[41],",":[43,64,77,125,147,191,326,351,396],"we":[44,269],"give":[45],"infinite":[51],"family":[52],"error-correcting":[54],"rate":[57],"notation=\"LaTeX\">$R$":[62],"over":[65],"size":[69,96,331],"notation=\"LaTeX\">$(1/\\epsilon)^{O(1/\\epsilon":[74],"^{2})}$":[75],"that":[78,297,328,357],"can":[79,112,154,175,332],"be":[80,113,155,176,334],"decoded":[82],"from":[83],"a":[84,132,149,233,279,288,318,337,345,354,366],"notation=\"LaTeX\">$(1-R-\\epsilon)$":[89],"-fraction":[91],"errors":[93],"at":[97,137],"most":[98,138],"notation=\"LaTeX\">$\\exp":[103,209],"(\\mathrm":[104,210],"{poly}(1/":[105,122,144,188,211],"\\epsilon))$":[106],".":[108,168,218],"Moreover,":[109],"the":[110,126,195,199,283,298,315,329,341,359,384],"encoded":[114],"in":[115,131,157,178,237,310,365],"time":[116,158,204],"notation=\"LaTeX\">$\\mathrm":[121,143,163,187],"\\epsilon,n)$":[123,189],"output":[127,299],"is":[129,296,308,353],"contained":[130,309],"linear":[133,291],"subspace":[134,153,196,356,386],"dimension":[136],"\\epsilon)$":[145],"basis":[150],"this":[152],"found":[156],"{poly}(1":[164],"/\\epsilon,":[165],"n)$":[166],"Thus,":[169],"both":[170],"encoding":[171],"decoding":[174],"performed":[177],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">fully":[181],"polynomial-time</i>":[182],"except":[192],"pruning":[194],"outputting":[198],"final":[200],"which":[202,352],"takes":[203],"\\epsilon))":[212],"\\cdot":[213],"\\mathrm":[214],"{poly}":[215],"(n)$":[216],"In":[219],"contrast,":[220],"prior":[221],"constructions":[225],"either":[231],"required":[232],"much":[234,251],"higher":[235],"complexity":[236],"terms":[238],"notation=\"LaTeX\">$1/":[244],"\\epsilon":[245],"$":[246],"(and":[248],"were":[249],"additionally":[250],"less":[252],"structured),":[253],"or":[254,258],"had":[255],"super-constant":[256],"Our":[261,293],"are":[263],"quite":[264],"natural":[265],"structured.":[267],"Specifically,":[268],"use":[270],"algebraic-geometric":[271],"(AG)":[272],"evaluation":[275,306],"points":[276,307],"restricted":[277,286],"to":[278,287,336,344,375],"subfield,":[280],"message":[284,342],"space":[285,343],"(carefully":[289],"chosen)":[290],"subspace.":[292],"main":[294],"observation":[295],"AG":[302],"subfield":[305],"affine":[312],"shift":[313],"image":[316,360],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">block-triangular-Toeplitz</i>":[321],"(BTT)":[322],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">matrix</i>":[325],"potentially":[333],"reduced":[335],"by":[339],"restricting":[340],"BTT":[346,363,379],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">evasive":[349],"subspace</i>":[350],"large":[355],"intersects":[358],"matrix":[364],"number":[368],"points.":[370],"further":[372],"show":[373],"how":[374],"explicitly":[376],"construct":[377],"such":[378],"evasive":[380],"subspaces,":[381],"based":[382],"on":[383],"designs":[387],"Guruswami":[389],"Kopparty":[391],"(":[392],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Combinatorica</i>":[395],"2016),":[397],"composition.":[399]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2020-11-23T00:00:00"}