{"id":"https://openalex.org/W2975566198","doi":"https://doi.org/10.1109/tit.2021.3071597","title":"A Moment Ratio Bound for Polynomials and Some Extremal Properties of Krawchouk Polynomials and Hamming Spheres","display_name":"A Moment Ratio Bound for Polynomials and Some Extremal Properties of Krawchouk Polynomials and Hamming Spheres","publication_year":2021,"publication_date":"2021-04-07","ids":{"openalex":"https://openalex.org/W2975566198","doi":"https://doi.org/10.1109/tit.2021.3071597","mag":"2975566198"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3071597","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3071597","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1909.11929","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056760639","display_name":"Naomi Kirshner","orcid":null},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Naomi Kirshner","raw_affiliation_strings":["School of Engineering and Computer Science, The Hebrew University of Jerusalem, Jerusalem, Israel","[School of Engineering and Computer Science, The Hebrew University of Jerusalem, Jerusalem, Israel]"],"affiliations":[{"raw_affiliation_string":"School of Engineering and Computer Science, The Hebrew University of Jerusalem, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"[School of Engineering and Computer Science, The Hebrew University of Jerusalem, Jerusalem, Israel]","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004360801","display_name":"Alex Samorodnitsky","orcid":"https://orcid.org/0000-0001-8643-7948"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Alex Samorodnitsky","raw_affiliation_strings":["School of Engineering and Computer Science, The Hebrew University of Jerusalem, Jerusalem, Israel","[School of Engineering and Computer Science, The Hebrew University of Jerusalem, Jerusalem, Israel]"],"affiliations":[{"raw_affiliation_string":"School of Engineering and Computer Science, The Hebrew University of Jerusalem, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"[School of Engineering and Computer Science, The Hebrew University of Jerusalem, Jerusalem, Israel]","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056760639"],"corresponding_institution_ids":["https://openalex.org/I197251160"],"apc_list":null,"apc_paid":null,"fwci":0.98772503,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.79184593,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"67","issue":"6","first_page":"3509","last_page":"3541"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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":0.9994000196456909,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7810510396957397},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.718298077583313},{"id":"https://openalex.org/keywords/hamming-bound","display_name":"Hamming bound","score":0.6934741735458374},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.600239634513855},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.5472358465194702},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5277460217475891},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.47865092754364014},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.44690391421318054},{"id":"https://openalex.org/keywords/hamming-space","display_name":"Hamming space","score":0.4451846778392792},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38094741106033325},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19055050611495972},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1394512951374054},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.11381003260612488},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07305672764778137}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7810510396957397},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.718298077583313},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.6934741735458374},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.600239634513855},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.5472358465194702},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5277460217475891},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.47865092754364014},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44690391421318054},{"id":"https://openalex.org/C2779494224","wikidata":"https://www.wikidata.org/wiki/Q5645799","display_name":"Hamming space","level":5,"score":0.4451846778392792},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38094741106033325},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19055050611495972},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1394512951374054},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.11381003260612488},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07305672764778137},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tit.2021.3071597","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3071597","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":"pmh:oai:arXiv.org:1909.11929","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.11929","pdf_url":"https://arxiv.org/pdf/1909.11929","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":null,"raw_type":"text"},{"id":"mag:2975566198","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1909.11929","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1909.11929","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1909.11929","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"},{"id":"mag:3155034568","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/journals/eccc/eccc26.html#KirshnerS19","pdf_url":null,"source":{"id":"https://openalex.org/S4306509107","display_name":"Electron. Colloquium Comput. Complex.","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Electron. Colloquium Comput. Complex.","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1909.11929","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.11929","pdf_url":"https://arxiv.org/pdf/1909.11929","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2975566198.pdf","grobid_xml":"https://content.openalex.org/works/W2975566198.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W109405981","https://openalex.org/W1550204818","https://openalex.org/W1601285146","https://openalex.org/W1891181203","https://openalex.org/W1981075218","https://openalex.org/W1990876436","https://openalex.org/W2015343723","https://openalex.org/W2028652233","https://openalex.org/W2036600344","https://openalex.org/W2043819676","https://openalex.org/W2063054346","https://openalex.org/W2069918448","https://openalex.org/W2074734756","https://openalex.org/W2078929687","https://openalex.org/W2081256580","https://openalex.org/W2088641045","https://openalex.org/W2088668281","https://openalex.org/W2094654291","https://openalex.org/W2098392316","https://openalex.org/W2103749128","https://openalex.org/W2109084006","https://openalex.org/W2131499713","https://openalex.org/W2159038374","https://openalex.org/W2169207476","https://openalex.org/W2178016547","https://openalex.org/W2327680971","https://openalex.org/W2334237942","https://openalex.org/W2488143187","https://openalex.org/W2591190829","https://openalex.org/W2802429607","https://openalex.org/W2856771174","https://openalex.org/W2949874440","https://openalex.org/W2964326154","https://openalex.org/W2965725349","https://openalex.org/W2972035503","https://openalex.org/W3038165843","https://openalex.org/W3081090248","https://openalex.org/W3102754027","https://openalex.org/W4229826396","https://openalex.org/W6635811265","https://openalex.org/W6748373802","https://openalex.org/W6751441677","https://openalex.org/W6752906924"],"related_works":["https://openalex.org/W3155034568","https://openalex.org/W1891181203","https://openalex.org/W2163010692","https://openalex.org/W3081090248","https://openalex.org/W2170862660","https://openalex.org/W2167345614","https://openalex.org/W2980661231","https://openalex.org/W2963930236","https://openalex.org/W2034968281","https://openalex.org/W1976116479","https://openalex.org/W2951171881","https://openalex.org/W2032742263","https://openalex.org/W2892564615","https://openalex.org/W2953025120","https://openalex.org/W49309924","https://openalex.org/W2741595416","https://openalex.org/W2341536123","https://openalex.org/W2532246700","https://openalex.org/W2510524578","https://openalex.org/W2953261448"],"abstract_inverted_index":{"Let":[0],"$p":[1,51],"\\ge":[2],"2$.":[3],"We":[4,58,238],"improve":[5,251],"the":[6,19,28,60,72,98,105,123,145,172,206,224,235,253,263,270],"bound":[7,62],"$\\frac{\\|f\\|_p}{\\|f\\|_2}":[8],"\\le":[9,131,133,141,143],"(p-1)^{s/2}$":[10],"for":[11,49,71,136,187,246,281],"a":[12,67,154,177,216,220,241,266],"polynomial":[13,74],"$f$":[14],"of":[15,32,40,75,83,104,148,157,162,171,205,227,234,243,265,284],"degree":[16,76,107],"$s$":[17,150],"on":[18,248,252],"boolean":[20],"cube":[21],"$\\{0,1\\}^n$,":[22,249],"which":[23,44,250,277],"comes":[24],"from":[25],"hypercontractivity,":[26],"replacing":[27],"right":[29],"hand":[30],"side":[31],"this":[33,213],"inequality":[34,258],"by":[35,259],"an":[36],"explicit":[37],"bivariate":[38],"function":[39,267],"$p$":[41],"and":[42,54,86,108,135,182,276],"$s$,":[43],"is":[45,176],"smaller":[46,68],"than":[47],"$(p-1)^{s/2}$":[48],"any":[50],">":[52,56],"2$":[53],"$s":[55],"0$.":[57],"show":[59],"new":[61],"to":[63,113,153,201],"be":[64,114],"tight,":[65],"within":[66],"order":[69],"factor,":[70],"Krawchouk":[73,84,94],"$s$.":[77],"This":[78,190],"implies":[79,192],"several":[80],"nearly-extremal":[81],"properties":[82],"polynomials":[85,95,103],"Hamming":[87,90,120,146,194,217,221,285],"spheres":[88,121,195],"(equivalently,":[89],"balls).":[91],"In":[92,209],"particular,":[93],"have":[96,122],"(almost)":[97,197],"heaviest":[99],"tails":[100],"among":[101,169,203,230],"all":[102,129,137,231],"same":[106,173,207,236],"$\\ell_2$":[109],"norm":[110],"(this":[111],"has":[112,223],"interpreted":[115],"with":[116,199],"some":[117],"care).":[118],"The":[119],"following":[124],"approximate":[125],"edge-isoperimetric":[126],"property:":[127],"For":[128],"$1":[130],"s":[132],"\\frac{n}{2}$,":[134],"even":[138],"distances":[139],"$0":[140],"i":[142],"\\frac{2s(n-s)}{n}$,":[144],"sphere":[147,218],"radius":[149],"contains,":[151],"up":[152],"multiplicative":[155],"factor":[156],"$O(i)$,":[158],"as":[159,167,269],"many":[160],"pairs":[161],"points":[163],"at":[164],"distance":[165],"$i$":[166],"possible,":[168],"sets":[170,204],"size":[174],"(there":[175],"similar,":[178],"but":[179],"slightly":[180],"weaker":[181],"somewhat":[183],"more":[184],"complicated":[185],"claim":[186],"general":[188],"distances).":[189],"also":[191,239],"that":[193,215],"are":[196,278],"stablest":[198],"respect":[200],"noise":[202],"size.":[208],"coding":[210],"theory":[211],"terms":[212],"means":[214],"(equivalently":[219],"ball)":[222],"maximal":[225],"probability":[226],"undetected":[228],"error,":[229],"binary":[232],"codes":[233],"rate.":[237],"describe":[240],"family":[242],"hypercontractive":[244],"inequalities":[245],"functions":[247,283],"`usual'":[254],"\"$q":[255],"\\rightarrow":[256],"2$\"":[257],"taking":[260],"into":[261],"account":[262],"concentration":[264],"(expressed":[268],"ratio":[271],"between":[272],"its":[273],"$\\ell_r$":[274],"norms),":[275],"nearly":[279],"tight":[280],"characteristic":[282],"spheres.":[286]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}