{"id":"https://openalex.org/W2037558448","doi":"https://doi.org/10.1017/s0963548306007589","title":"Autocorrelations of Random Binary Sequences","display_name":"Autocorrelations of Random Binary Sequences","publication_year":2006,"publication_date":"2006-07-31","ids":{"openalex":"https://openalex.org/W2037558448","doi":"https://doi.org/10.1017/s0963548306007589","mag":"2037558448"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548306007589","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548306007589","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-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/A5073977028","display_name":"Idris Mercer","orcid":null},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"IDRIS DAVID MERCER","raw_affiliation_strings":["Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada V5A 1S6 (e-mail:","Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada V5A 1S6 (e-mail: idmercer@math.sfu.ca)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada V5A 1S6 (e-mail:","institution_ids":["https://openalex.org/I18014758"]},{"raw_affiliation_string":"Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada V5A 1S6 (e-mail: idmercer@math.sfu.ca)","institution_ids":["https://openalex.org/I18014758"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073977028"],"corresponding_institution_ids":["https://openalex.org/I18014758"],"apc_list":null,"apc_paid":null,"fwci":5.4405,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.95834711,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"15","issue":"5","first_page":"663","last_page":"671"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9980000257492065,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.8008404970169067},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.7113980054855347},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6489755511283875},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6444969773292542},{"id":"https://openalex.org/keywords/tuple","display_name":"Tuple","score":0.626388430595398},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.517665445804596},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5147028565406799},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4932329058647156},{"id":"https://openalex.org/keywords/pseudorandom-binary-sequence","display_name":"Pseudorandom binary sequence","score":0.4504564106464386},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4197627007961273},{"id":"https://openalex.org/keywords/expected-value","display_name":"Expected value","score":0.41749852895736694},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4149370491504669},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3980821371078491},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18022724986076355},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.10168370604515076},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08949393033981323}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8008404970169067},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.7113980054855347},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6489755511283875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6444969773292542},{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.626388430595398},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.517665445804596},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5147028565406799},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4932329058647156},{"id":"https://openalex.org/C128040838","wikidata":"https://www.wikidata.org/wiki/Q1810628","display_name":"Pseudorandom binary sequence","level":3,"score":0.4504564106464386},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4197627007961273},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.41749852895736694},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4149370491504669},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3980821371078491},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18022724986076355},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.10168370604515076},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08949393033981323},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548306007589","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548306007589","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W190050568","https://openalex.org/W1509536479","https://openalex.org/W1520303766","https://openalex.org/W1545693521","https://openalex.org/W1546372806","https://openalex.org/W1566820429","https://openalex.org/W1968734093","https://openalex.org/W2020275256","https://openalex.org/W2065609889","https://openalex.org/W2068871408","https://openalex.org/W2135570981","https://openalex.org/W2142732204","https://openalex.org/W2143943120","https://openalex.org/W2399991609"],"related_works":["https://openalex.org/W57364028","https://openalex.org/W2047057931","https://openalex.org/W2545761980","https://openalex.org/W170825502","https://openalex.org/W4285709129","https://openalex.org/W2049621396","https://openalex.org/W2066502241","https://openalex.org/W2354392213","https://openalex.org/W4249913278","https://openalex.org/W4382516233"],"abstract_inverted_index":{"We":[0,162],"define":[1,37,90],"${\\mathcal":[2],"B}_n$":[3,27],"to":[4,74,110],"be":[5],"the":[6,12,38,124,132,145,151,172],"set":[7],"of":[8,11,40,57,76,106,148,171],"$n$":[9],"-tuples":[10],"form":[13],"$(a_0,":[14],"{\\ldots}\\,,":[15],"a_{n-1})$":[16],"where":[17],"$a_j":[18],"=":[19,177],"\\pm":[20],"1$":[21,85,156],".":[22,54,179],"If":[23],"$A":[24],"\\in":[25,95],"{\\mathcal":[26,96],",":[28],"then":[29],"we":[30,89,120,136],"call":[31],"$A$":[32,41],"a":[33],"binary":[34,59],"sequence":[35],"and":[36,70,78,135,141],"autocorrelations":[39,62],"by":[42],"$c_k":[43],":=":[44,93],"\\sum_{j=0}^{n-k-1}":[45],"a_j":[46],"a_{j+k}$":[47],"for":[48,144],"$0":[49],"\\leq":[50,52,99,101],"k":[51,100],"n-1$":[53],"The":[55,104],"problem":[56],"finding":[58],"sequences":[60],"with":[61,83,159],"\u2018near":[63],"zero\u2019":[64],"has":[65],"arisen":[66],"in":[67,131,169],"communications":[68],"engineering":[69],"is":[71,109],"also":[72,163],"relevant":[73],"conjectures":[75],"Littlewood":[77],"Erd\u0151s":[79],"on":[80,128],"\u2018flat\u2019":[81],"polynomials":[82],"$\\pm":[84,155],"coefficients.":[86],"Following":[87],"Turyn,":[88],"\\[":[91],"b(n)":[92],"\\min_{A":[94],"B}_n}":[97],"\\max_{1":[98],"n-1}":[102],"|c_k|.\\]":[103],"purpose":[105],"this":[107],"article":[108],"show":[111],"that,":[112],"using":[113],"some":[114,165],"known":[115],"techniques":[116],"from":[117],"discrete":[118],"probability,":[119],"can":[121,137],"improve":[122],"upon":[123],"best":[125],"upper":[126],"bound":[127],"$b(n)$":[129],"appearing":[130],"previous":[133],"literature,":[134],"obtain":[138],"both":[139],"asymptotic":[140],"exact":[142],"expressions":[143],"expected":[146],"value":[147],"$c_k^m$":[149],"if":[150],"$a_j$":[152],"are":[153],"independent":[154],"random":[157],"variables":[158],"mean":[160],"0.":[161],"include":[164],"brief":[166],"heuristic":[167],"remarks":[168],"support":[170],"unproved":[173],"conjecture":[174],"that":[175],"$b(n)":[176],"O(\\sqrt{n})$":[178]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}