{"id":"https://openalex.org/W2792174692","doi":"https://doi.org/10.1109/tit.2018.2795608","title":"Large Sets of Disjoint Spectra Plateaued Functions Inequivalent to Partially Linear Functions","display_name":"Large Sets of Disjoint Spectra Plateaued Functions Inequivalent to Partially Linear Functions","publication_year":2018,"publication_date":"2018-01-19","ids":{"openalex":"https://openalex.org/W2792174692","doi":"https://doi.org/10.1109/tit.2018.2795608","mag":"2792174692"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2018.2795608","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2795608","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/A5056616258","display_name":"Fengrong Zhang","orcid":"https://orcid.org/0000-0002-6804-6975"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]},{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fengrong Zhang","raw_affiliation_strings":["School of Computer Science and Technology, China University of Mining and Technology, Xuzhou, China","State Key Laboratory of Integrated Services Networks, Xidian University, Xian, China"],"raw_orcid":"https://orcid.org/0000-0002-6804-6975","affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, China University of Mining and Technology, Xuzhou, China","institution_ids":["https://openalex.org/I25757504"]},{"raw_affiliation_string":"State Key Laboratory of Integrated Services Networks, Xidian University, Xian, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027674774","display_name":"Yongzhuang Wei","orcid":"https://orcid.org/0000-0002-3371-4865"},"institutions":[{"id":"https://openalex.org/I4210132990","display_name":"State Key Laboratory of Cryptology","ror":"https://ror.org/02pn5rj08","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210132990"]},{"id":"https://openalex.org/I5343935","display_name":"Guilin University of Electronic Technology","ror":"https://ror.org/05arjae42","country_code":"CN","type":"education","lineage":["https://openalex.org/I5343935"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongzhuang Wei","raw_affiliation_strings":["Guangxi Colleges and Universities Key Laboratory of Cloud Computing and Complex Systems, Guilin University of Electronic Technology, Guilin, China","Guangxi Key Laboratory of Cryptography and Information Security"],"raw_orcid":"https://orcid.org/0000-0002-3371-4865","affiliations":[{"raw_affiliation_string":"Guangxi Colleges and Universities Key Laboratory of Cloud Computing and Complex Systems, Guilin University of Electronic Technology, Guilin, China","institution_ids":["https://openalex.org/I5343935"]},{"raw_affiliation_string":"Guangxi Key Laboratory of Cryptography and Information Security","institution_ids":["https://openalex.org/I4210132990"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039271966","display_name":"Enes Pa\u0161ali\u0107","orcid":"https://orcid.org/0000-0001-6343-8796"},"institutions":[{"id":"https://openalex.org/I118905719","display_name":"University of Primorska","ror":"https://ror.org/05xefg082","country_code":"SI","type":"education","lineage":["https://openalex.org/I118905719"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Enes Pasalic","raw_affiliation_strings":["FAMNIT and IAM, University of Primorska, Koper, Slovenia"],"raw_orcid":"https://orcid.org/0000-0001-6343-8796","affiliations":[{"raw_affiliation_string":"FAMNIT and IAM, University of Primorska, Koper, Slovenia","institution_ids":["https://openalex.org/I118905719"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102732396","display_name":"Shixiong Xia","orcid":"https://orcid.org/0000-0002-3952-0877"},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shixiong Xia","raw_affiliation_strings":["School of Computer Science and Technology, China University of Mining and Technology, Xuzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, China University of Mining and Technology, Xuzhou, China","institution_ids":["https://openalex.org/I25757504"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5808,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.91560083,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"64","issue":"4","first_page":"2987","last_page":"2999"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9984999895095825,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9807000160217285,"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/disjoint-sets","display_name":"Disjoint sets","score":0.9439247846603394},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.7676327228546143},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6898796558380127},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.6811323761940002},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5781106948852539},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5003349781036377},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4832492470741272},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4586309492588043},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45765626430511475},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18468809127807617},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10990622639656067}],"concepts":[{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.9439247846603394},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.7676327228546143},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6898796558380127},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.6811323761940002},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5781106948852539},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5003349781036377},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4832492470741272},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4586309492588043},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45765626430511475},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18468809127807617},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10990622639656067},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"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/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2018.2795608","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2795608","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1488367145","https://openalex.org/W1524430769","https://openalex.org/W1550410240","https://openalex.org/W1571032422","https://openalex.org/W1575067221","https://openalex.org/W1606480398","https://openalex.org/W1980279697","https://openalex.org/W1998858124","https://openalex.org/W2000857313","https://openalex.org/W2004788714","https://openalex.org/W2021737323","https://openalex.org/W2025123078","https://openalex.org/W2031388254","https://openalex.org/W2082960263","https://openalex.org/W2090432705","https://openalex.org/W2093326553","https://openalex.org/W2095027936","https://openalex.org/W2099870437","https://openalex.org/W2121178597","https://openalex.org/W2136607390","https://openalex.org/W2139312425","https://openalex.org/W2154271831","https://openalex.org/W2304817441","https://openalex.org/W2395557130","https://openalex.org/W2399862786","https://openalex.org/W2504274129","https://openalex.org/W2528819694","https://openalex.org/W2614080401","https://openalex.org/W2733934550","https://openalex.org/W3098014432","https://openalex.org/W4298109338","https://openalex.org/W6630621434","https://openalex.org/W6634282481","https://openalex.org/W6634288471"],"related_works":["https://openalex.org/W132109778","https://openalex.org/W1989984537","https://openalex.org/W2499670206","https://openalex.org/W47687724","https://openalex.org/W2212615093","https://openalex.org/W24519920","https://openalex.org/W2999312112","https://openalex.org/W2346253477","https://openalex.org/W2087778462","https://openalex.org/W1909384579"],"abstract_inverted_index":{"In":[0,98,138],"this":[1,62],"paper,":[2],"we":[3,111,154,181],"give":[4,112],"an":[5,113],"efficient":[6],"method":[7,72,153],"for":[8,116],"constructing":[9],"a":[10,37,65,71,104],"large":[11,38],"set":[12,39],"of":[13,40,68,73,93,106,119,123,165],"disjoint":[14,41,76,120],"spectra":[15,42,77,121],"functions":[16,43,78,122,133,147,161,185],"without":[17],"linear":[18,26,51,136],"structures,":[19],"which":[20,44],"are":[21,45],"not":[22,46],"equivalent":[23,48],"to":[24,35],"partially":[25,50],"functions.":[27,97],"This":[28],"positively":[29],"answers":[30],"the":[31,59,91,99,107,149,175,192],"open":[32],"problem":[33],"[\u201chow":[34],"construct":[36],"(linearly":[47],"to)":[49],"functions\u201d":[52],"raised":[53],"by":[54],"Zhang":[55],"and":[56],"Xiao].":[57],"At":[58],"same":[60],"time,":[61],"significantly":[63],"extends":[64],"recent":[66],"result":[67],"Zhang,":[69],"where":[70],"specifying":[74],"four":[75],"was":[79],"given.":[80],"It":[81],"is":[82,141],"demonstrated":[83],"that":[84,143,189],"such":[85],"sets":[86,118],"can":[87,155],"be":[88],"utilized":[89],"in":[90,148,171],"design":[92,182],"highly":[94,157],"nonlinear":[95,158],"resilient":[96,159],"second":[100],"part,":[101],"based":[102],"on":[103],"generalization":[105],"indirect":[108,151],"sum":[109,152],"method,":[110],"alternative":[114],"approach":[115],"designing":[117],"even":[124],"larger":[125],"cardinality":[126],"than":[127],"already":[128],"given":[129],"ones,":[130],"but":[131],"these":[132],"then":[134],"admit":[135],"structures.":[137],"addition,":[139],"it":[140],"shown":[142],"using":[144],"suitable":[145],"initial":[146],"generalized":[150],"specify":[156],"Boolean":[160],"(in":[162],"odd":[163,187],"number":[164],"input":[166],"variables":[167],"n)":[168,188],"whose":[169],"nonlinearity":[170,194],"many":[172],"cases":[173],"exceeds":[174],"current":[176],"best":[177],"known":[178],"values.":[179],"Moreover,":[180],"some":[183],"balanced":[184],"(for":[186],"also":[190],"achieve":[191],"highest":[193],"known.":[195]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}