{"id":"https://openalex.org/W2029762703","doi":"https://doi.org/10.1109/tit.2012.2197812","title":"Improved Constructions of Frameproof Codes","display_name":"Improved Constructions of Frameproof Codes","publication_year":2012,"publication_date":"2012-06-07","ids":{"openalex":"https://openalex.org/W2029762703","doi":"https://doi.org/10.1109/tit.2012.2197812","mag":"2029762703"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2012.2197812","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2197812","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":["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/A5088037430","display_name":"Yeow Meng Chee","orcid":"https://orcid.org/0000-0001-7823-8068"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Yeow Meng Chee","raw_affiliation_strings":["Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","[Sch. of Phys. & Math. Sci., Nanyang Technol. Univ., Singapore, Singapore]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"[Sch. of Phys. & Math. Sci., Nanyang Technol. Univ., Singapore, Singapore]","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046105120","display_name":"Xiande Zhang","orcid":"https://orcid.org/0000-0003-4234-3610"},"institutions":[{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Xiande Zhang","raw_affiliation_strings":["School of Mathematical Sciences, Monash University, VIC, Australia","Sch. of Math. Sci., Monash Univ., Clayton, VIC, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Monash University, VIC, Australia","institution_ids":["https://openalex.org/I56590836"]},{"raw_affiliation_string":"Sch. of Math. Sci., Monash Univ., Clayton, VIC, Australia","institution_ids":["https://openalex.org/I56590836"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.859,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.76747615,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"58","issue":"8","first_page":"5449","last_page":"5453"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10388","display_name":"Advanced Steganography and Watermarking Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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/T11130","display_name":"Coding theory and cryptography","score":0.9990000128746033,"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/T12029","display_name":"DNA and Biological Computing","score":0.9988999962806702,"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/alphabet","display_name":"Alphabet","score":0.4993712902069092},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3670436143875122},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3614237308502197},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3536084294319153},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2715257406234741},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.1480153501033783}],"concepts":[{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.4993712902069092},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3670436143875122},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3614237308502197},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3536084294319153},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2715257406234741},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.1480153501033783},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2012.2197812","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2197812","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:CiteSeerX.psu:10.1.1.721.9126","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.721.9126","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www1.spms.ntu.edu.sg/%7Eymchee/papers/frameproof.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.760.4938","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.760.4938","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1206.5863.pdf","raw_type":"text"},{"id":"pmh:oai:dr.ntu.edu.sg:10356/95980","is_oa":false,"landing_page_url":"https://hdl.handle.net/10220/11423","pdf_url":null,"source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"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":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W286861583","https://openalex.org/W1970997983","https://openalex.org/W1977041010","https://openalex.org/W1977383963","https://openalex.org/W1995096771","https://openalex.org/W2001092675","https://openalex.org/W2002087984","https://openalex.org/W2018821316","https://openalex.org/W2037003834","https://openalex.org/W2067182672","https://openalex.org/W2091887150","https://openalex.org/W2122882636","https://openalex.org/W2124938909","https://openalex.org/W2134195444","https://openalex.org/W2154572525","https://openalex.org/W2165902826","https://openalex.org/W2166399930","https://openalex.org/W2911455720","https://openalex.org/W2911546054","https://openalex.org/W4230677855","https://openalex.org/W4239254142"],"related_works":["https://openalex.org/W4225463470","https://openalex.org/W2774905398","https://openalex.org/W303980170","https://openalex.org/W2351491280","https://openalex.org/W2386767533","https://openalex.org/W2072668710","https://openalex.org/W4220791713","https://openalex.org/W2371447506","https://openalex.org/W3186821417","https://openalex.org/W4287064374"],"abstract_inverted_index":{"Frameproof":[0],"codes":[1,96,121],"are":[2],"used":[3],"to":[4,102],"preserve":[5],"the":[6,9,24,103,115,155],"security":[7],"in":[8],"context":[10],"of":[11,27,32,97,110,122],"coalition":[12],"when":[13,66,74,136,142],"fingerprinting":[14],"digital":[15],"data.":[16],"Let":[17],"M":[18,44],"<sub":[19,37,41,45,62,70,82,150],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[20,38,42,46,50,63,71,83,129,151],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">c,l</sub>":[21,39,47,64,72],"(q)":[22],"be":[23],"largest":[25],"cardinality":[26],"a":[28,91,169],"q-ary":[29,119],"c-frameproof":[30,95,120],"code":[31],"length":[33,98,123],"l":[34,77,99],"and":[35,76,80,125,138],"R":[36,61,69,81,149],"=lim":[40],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q\u2192\u221e</sub>":[43],"(q)/q":[48],"<sup":[49,128],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">[":[51],"l/c]</sup>":[52],".":[53,107,144],"It":[54],"has":[55],"been":[56],"determined":[57],"by":[58,159],"Blackburn":[59],"that":[60,148,166],"=1":[65],"l\u22611(mod":[67],"c),":[68],"=2":[73],"c=2":[75,137],"is":[78,168],"even,":[79],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">3,5</sub>":[84],"=5/3.":[85],"In":[86],"this":[87,111],"paper,":[88],"we":[89,113,146],"give":[90],"recursive":[92],"construction":[93],"for":[94,118,132,139,161],"with":[100],"respect":[101],"alphabet":[104],"size":[105,126],"q":[106,135],"As":[108],"applications":[109],"construction,":[112],"establish":[114],"existence":[116],"results":[117],"c+2":[124],"c+2/c(q-1)":[127],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[130],"+1":[131],"all":[133,140,162],"odd":[134],"q\u22614":[141],"c=3":[143],"Furthermore,":[145],"show":[147],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">c,c+2</sub>":[152],"=(c+2)/c":[153],"meeting":[154],"upper":[156],"bound":[157],"given":[158],"Blackburn,":[160],"integers":[163],"c":[164],"such":[165],"c+1":[167],"prime":[170],"power.":[171]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
