{"id":"https://openalex.org/W2788702912","doi":"https://doi.org/10.1142/s0129054117500265","title":"On the Conjecture About the Linear Structures of Rotation Symmetric Boolean Functions","display_name":"On the Conjecture About the Linear Structures of Rotation Symmetric Boolean Functions","publication_year":2017,"publication_date":"2017-11-01","ids":{"openalex":"https://openalex.org/W2788702912","doi":"https://doi.org/10.1142/s0129054117500265","mag":"2788702912"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054117500265","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054117500265","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","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/A5101926392","display_name":"Lei Sun","orcid":"https://orcid.org/0000-0003-1992-5225"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lei Sun","raw_affiliation_strings":["Chern Institute of Mathematics, Nankai University, Tianjin 300071, P. R. China"],"affiliations":[{"raw_affiliation_string":"Chern Institute of Mathematics, Nankai University, Tianjin 300071, P. R. China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063946169","display_name":"Fang\u2010Wei Fu","orcid":"https://orcid.org/0000-0002-9696-8977"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fangwei Fu","raw_affiliation_strings":["Chern Institute of Mathematics, Nankai University, Tianjin 300071, P. R. China"],"affiliations":[{"raw_affiliation_string":"Chern Institute of Mathematics, Nankai University, Tianjin 300071, P. R. China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100414637","display_name":"Jian Liu","orcid":"https://orcid.org/0000-0001-9104-2975"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Liu","raw_affiliation_strings":["School of Computer Software, Tianjin University, Tianjin 300350, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Computer Software, Tianjin University, Tianjin 300350, P. R. China","institution_ids":["https://openalex.org/I162868743"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101926392"],"corresponding_institution_ids":["https://openalex.org/I205237279"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.22234962,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"28","issue":"07","first_page":"819","last_page":"833"},"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":0.9929999709129333,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9857000112533569,"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/conjecture","display_name":"Conjecture","score":0.839348316192627},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7890803813934326},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.5983144640922546},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5179009437561035},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5057456493377686},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.4436420798301697},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.4380495548248291},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4342947006225586},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4215139150619507},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4125863313674927},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3928954005241394},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06265220046043396}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.839348316192627},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7890803813934326},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.5983144640922546},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5179009437561035},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5057456493377686},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.4436420798301697},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.4380495548248291},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4342947006225586},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4215139150619507},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4125863313674927},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3928954005241394},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06265220046043396},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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":1,"locations":[{"id":"doi:10.1142/s0129054117500265","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054117500265","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1292825847","display_name":null,"funder_award_id":"61171082","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2301527561","display_name":null,"funder_award_id":"61571243","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W131501431","https://openalex.org/W1605416950","https://openalex.org/W1963781702","https://openalex.org/W1965797160","https://openalex.org/W1972892810","https://openalex.org/W1980279697","https://openalex.org/W2031388254","https://openalex.org/W2129409147","https://openalex.org/W2154271831","https://openalex.org/W2309179828","https://openalex.org/W2316868047","https://openalex.org/W4238806542","https://openalex.org/W4292003697"],"related_works":["https://openalex.org/W2964230509","https://openalex.org/W2785232145","https://openalex.org/W2092886012","https://openalex.org/W2145874891","https://openalex.org/W2170281757","https://openalex.org/W2790802381","https://openalex.org/W2119028753","https://openalex.org/W1982026196","https://openalex.org/W2511750106","https://openalex.org/W3194134751"],"abstract_inverted_index":{"In":[0],"this":[1,33],"paper,":[2],"we":[3],"study":[4],"the":[5,42,50,59,73],"conjecture":[6,74,86],"that":[7,31,72],"[Formula:":[8,21,55,78],"see":[9,12,22,56,79],"text]-variable":[10],"([Formula:":[11],"text]":[13,23,57],"odd)":[14],"rotation":[15],"symmetric":[16],"Boolean":[17],"functions":[18],"with":[19],"degree":[20,54],"have":[24,37],"no":[25],"non-zero":[26,38],"linear":[27,39,43,47],"structures.":[28],"We":[29],"show":[30],"if":[32],"class":[34],"of":[35,53],"RSBFs":[36],"structures,":[40],"then":[41,82],"structures":[44,48],"are":[45],"invariant":[46],"and":[49,81],"homogeneous":[51],"component":[52],"in":[58],"function\u2019s":[60],"algebraic":[61],"normal":[62],"form":[63],"has":[64],"only":[65],"two":[66],"possibilities.":[67],"Moreover,":[68],"it":[69],"is":[70,75,87],"checked":[71],"true":[76],"for":[77],"text],":[80],"a":[83],"more":[84],"explicit":[85],"proposed.":[88]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}