{"id":"https://openalex.org/W2156775423","doi":"https://doi.org/10.1109/tit.2015.2473848","title":"Probabilistic Existence Results for Separable Codes","display_name":"Probabilistic Existence Results for Separable Codes","publication_year":2015,"publication_date":"2015-09-22","ids":{"openalex":"https://openalex.org/W2156775423","doi":"https://doi.org/10.1109/tit.2015.2473848","mag":"2156775423"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2015.2473848","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2015.2473848","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"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1505.02597","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044763974","display_name":"Simon R. Blackburn\u22c6","orcid":"https://orcid.org/0000-0003-0762-031X"},"institutions":[{"id":"https://openalex.org/I184558857","display_name":"Royal Holloway University of London","ror":"https://ror.org/04g2vpn86","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I184558857"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Simon R. Blackburn","raw_affiliation_strings":["Department of Mathematics, Royal Holloway University of London, Egham, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Royal Holloway University of London, Egham, U.K","institution_ids":["https://openalex.org/I184558857"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5044763974"],"corresponding_institution_ids":["https://openalex.org/I184558857"],"apc_list":null,"apc_paid":null,"fwci":1.4949,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.88301033,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"61","issue":"11","first_page":"5822","last_page":"5827"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10388","display_name":"Advanced Steganography and Watermarking Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10388","display_name":"Advanced Steganography and Watermarking Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11269","display_name":"Algorithms and Data Compression","score":0.9965999722480774,"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/T11130","display_name":"Coding theory and cryptography","score":0.9919000267982483,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.8788610696792603},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7067951560020447},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6582366228103638},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49076828360557556},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.44398343563079834},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.416288822889328},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08587759733200073}],"concepts":[{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.8788610696792603},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7067951560020447},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6582366228103638},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49076828360557556},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44398343563079834},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.416288822889328},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08587759733200073},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2015.2473848","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2015.2473848","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:1505.02597","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1505.02597","pdf_url":"https://arxiv.org/pdf/1505.02597","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1505.02597","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1505.02597","pdf_url":"https://arxiv.org/pdf/1505.02597","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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W287817357","https://openalex.org/W1159056583","https://openalex.org/W1997166677","https://openalex.org/W2067182672","https://openalex.org/W2090770845","https://openalex.org/W2131762402","https://openalex.org/W2132482824","https://openalex.org/W2134195444","https://openalex.org/W2152545485","https://openalex.org/W2165902826","https://openalex.org/W2293452572","https://openalex.org/W2949376982","https://openalex.org/W3002515632","https://openalex.org/W3104897092","https://openalex.org/W4239254142","https://openalex.org/W6610403788","https://openalex.org/W6627365276","https://openalex.org/W6785732742"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2009525028","https://openalex.org/W4321064619","https://openalex.org/W2076561698","https://openalex.org/W2053599029","https://openalex.org/W2962925412","https://openalex.org/W2023672523","https://openalex.org/W4246719751","https://openalex.org/W2483165346","https://openalex.org/W3011179836"],"abstract_inverted_index":{"Separable":[0],"codes":[1,24,36,42,50,61,77,100,226,239],"were":[2],"defined":[3],"by":[4,11],"Cheng":[5],"and":[6,29,39,72,112,126,199,224,256],"Miao":[7],"in":[8,18,155,175],"2011,":[9],"motivated":[10],"applications":[12],"to":[13,197,261],"the":[14,158,163,171,189,252,264],"identification":[15],"of":[16,62,78,136,173,207,254,266,268,273],"pirates":[17],"a":[19,119,132,176,203,269],"multimedia":[20],"setting.":[21],"Combinatorially,":[22],"t\u0305-separable":[23,41,60,76,134,177],"lie":[25],"somewhere":[26],"between":[27],"t-frameproof":[28,35],"(t":[30,44,166],"-":[31,45,167,218],"1)-frameproof":[32,168],"codes:":[33],"all":[34,40,108,113,148],"are":[37,43,58,184],"t\u0305-separable,":[38],"1)-frameproof.":[46],"Results":[47,195],"for":[48,98,107,147],"frameproof":[49],"show":[51,201,262],"that":[52,73,129,157,202,225,251,263],"(when":[53],"q":[54,67,86,279,285],"is":[55,179,276],"large)":[56],"there":[57,117,130],"q-ary":[59,75,133,204,270],"length":[63,79,137,208,274],"n":[64,80,114,138,209,275],"with":[65,139,227],"approximately":[66,85],"<sup":[68,87,143,215,220,231,280,286,290],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[69,88,144,216,221,232,281,287,291],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">[n/t]</sup>":[70],"codewords,":[71,223],"no":[74],"can":[81,210,258],"have":[82],"more":[83,185],"than":[84],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">[n/(t-l)]</sup>":[89],"codewords.":[90],"This":[91,153,247],"paper":[92,248],"provides":[93],"improved":[94],"probabilistic":[95],"existence":[96],"results":[97,182],"t-separable":[99],"when":[101,191],"t":[102,109,125,192],"\u2265":[103,110,115],"3.":[104],"More":[105],"precisely,":[106],"3":[111],"3,":[116],"exists":[118,131],"constant":[120],"\u03ba":[121],"(depending":[122],"only":[123],"on":[124,165,170],"n),":[127],"such":[128],"code":[135,178,206,272],"at":[140,212,228,277],"least":[141,229],"\u03baq":[142,230],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n/(t-1)</sup>":[145],"codewords":[146,174,234,267],"sufficiently":[149],"large":[150],"integers":[151],"q.":[152],"shows,":[154],"particular,":[156],"upper":[159],"bound":[160,164,253],"[derived":[161],"from":[162],"codes]":[169],"number":[172,265],"realistic.":[180],"The":[181],"above":[183],"surprising":[186],"after":[187],"examining":[188],"situation":[190],"=":[193],"2.":[194],"due":[196],"Gao":[198,255],"Ge":[200,257],"2\u0305-separable":[205,238,271],"contain":[211],"most":[213,278],"3/2q":[214],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2[n/3]</sup>":[217],"1/2q":[219],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">[n/3]</sup>":[222,288,292],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2n/3</sup>":[233],"exist.":[235],"Thus,":[236],"optimal":[237],"behave":[240],"neither":[241],"like":[242],"two-frameproof":[243],"nor":[244],"one-frameproof":[245],"codes.":[246],"also":[249],"observes":[250],"be":[259],"strengthened":[260],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">[2n/3]</sup>":[282],"+":[283],"1/2":[284],"(q":[289],"-1).":[293]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
