{"id":"https://openalex.org/W2051961051","doi":"https://doi.org/10.1142/s0129054114500178","title":"ONE SUFFICIENT AND NECESSARY CONDITION ON BALANCED BOOLEAN FUNCTIONS WITH \u03c3<sub>f</sub> = 2<sup>2n</sup> + 2<sup>n+3</sup>(n \u2265 3)","display_name":"ONE SUFFICIENT AND NECESSARY CONDITION ON BALANCED BOOLEAN FUNCTIONS WITH \u03c3<sub>f</sub> = 2<sup>2n</sup> + 2<sup>n+3</sup>(n \u2265 3)","publication_year":2014,"publication_date":"2014-04-01","ids":{"openalex":"https://openalex.org/W2051961051","doi":"https://doi.org/10.1142/s0129054114500178","mag":"2051961051"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054114500178","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054114500178","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/A5041316526","display_name":"Yu Zhou","orcid":"https://orcid.org/0000-0003-1777-9439"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"YU ZHOU","raw_affiliation_strings":["Science and Technology on Communication Security Laboratory, Chengdu 610041, P. R. China"],"affiliations":[{"raw_affiliation_string":"Science and Technology on Communication Security Laboratory, Chengdu 610041, P. R. China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100403245","display_name":"Lin Wang","orcid":"https://orcid.org/0000-0003-2578-4502"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"LIN WANG","raw_affiliation_strings":["Science and Technology on Communication Security Laboratory, Chengdu 610041, P. R. China"],"affiliations":[{"raw_affiliation_string":"Science and Technology on Communication Security Laboratory, Chengdu 610041, P. R. China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081206878","display_name":"Weiqiong Wang","orcid":"https://orcid.org/0000-0002-9650-3563"},"institutions":[{"id":"https://openalex.org/I25355098","display_name":"Chang'an University","ror":"https://ror.org/05mxya461","country_code":"CN","type":"education","lineage":["https://openalex.org/I25355098"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"WEIQIONG WANG","raw_affiliation_strings":["School of Science, Chang'an University, Xi'an 710064, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Science, Chang'an University, Xi'an 710064, P. R. China","institution_ids":["https://openalex.org/I25355098"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100862227","display_name":"Xinfeng Dong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"XINFENG DONG","raw_affiliation_strings":["Science and Technology on Communication Security Laboratory, Chengdu 610041, P. R. China"],"affiliations":[{"raw_affiliation_string":"Science and Technology on Communication Security Laboratory, Chengdu 610041, P. R. China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101507366","display_name":"Xiaoni Du","orcid":"https://orcid.org/0000-0003-3997-7196"},"institutions":[{"id":"https://openalex.org/I68986083","display_name":"Northwest Normal University","ror":"https://ror.org/00gx3j908","country_code":"CN","type":"education","lineage":["https://openalex.org/I68986083"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"XIAONI DU","raw_affiliation_strings":["College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, P. R. China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, P. R. China","institution_ids":["https://openalex.org/I68986083"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5041316526"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.818,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.80720093,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"25","issue":"03","first_page":"343","last_page":"353"},"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9994999766349792,"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":0.9979000091552734,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.785728931427002},{"id":"https://openalex.org/keywords/explained-sum-of-squares","display_name":"Explained sum of squares","score":0.6836960911750793},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6563199758529663},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6262027621269226},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.6181521415710449},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5997076630592346},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5147461891174316},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5088048577308655},{"id":"https://openalex.org/keywords/boolean-network","display_name":"Boolean network","score":0.5086263418197632},{"id":"https://openalex.org/keywords/parity-function","display_name":"Parity function","score":0.4121130406856537},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.23460659384727478},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13382160663604736}],"concepts":[{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.785728931427002},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.6836960911750793},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6563199758529663},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6262027621269226},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6181521415710449},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5997076630592346},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5147461891174316},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5088048577308655},{"id":"https://openalex.org/C134444547","wikidata":"https://www.wikidata.org/wiki/Q585230","display_name":"Boolean network","level":3,"score":0.5086263418197632},{"id":"https://openalex.org/C188183281","wikidata":"https://www.wikidata.org/wiki/Q2898309","display_name":"Parity function","level":4,"score":0.4121130406856537},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.23460659384727478},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13382160663604736},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054114500178","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054114500178","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1966164580","https://openalex.org/W1983760747","https://openalex.org/W1986231753","https://openalex.org/W2075612964","https://openalex.org/W2091456407","https://openalex.org/W2099870437","https://openalex.org/W3098014432","https://openalex.org/W4292003697"],"related_works":["https://openalex.org/W2106622045","https://openalex.org/W2105128170","https://openalex.org/W1979056074","https://openalex.org/W2011175857","https://openalex.org/W2061512596","https://openalex.org/W52722086","https://openalex.org/W1991822629","https://openalex.org/W4252281389","https://openalex.org/W2918709778","https://openalex.org/W3141532631"],"abstract_inverted_index":{"The":[0],"Global":[1],"Avalanche":[2],"Characteristics":[3],"(including":[4],"the":[5,9,13,27,31,55,59,75,79,116,120],"sum-of-squares":[6,32,60,80,121],"indicator":[7,33,81,122],"and":[8,46,71],"absolute":[10],"indicator)":[11],"measure":[12],"overall":[14],"avalanche":[15],"characteristics":[16],"of":[17],"a":[18,35,44,50,92,110],"cryptographic":[19],"Boolean":[20,37,52,68,94],"function.":[21,38],"Son":[22],"et":[23],"al.":[24],"(1998)":[25],"gave":[26],"lower":[28,56,76,117],"bound":[29,57,118],"on":[30,49,58,78,119],"for":[34,98,125],"balanced":[36,51,67,93],"In":[39],"this":[40],"paper,":[41],"we":[42],"give":[43],"sufficient":[45],"necessary":[47],"condition":[48],"function":[53,95,114],"reaching":[54,115],"indicator.":[61],"We":[62,103],"also":[63],"analyze":[64],"whether":[65],"these":[66],"functions":[69],"exist,":[70],"if":[72],"they":[73],"reach":[74],"bounds":[77],"or":[82],"not.":[83],"Our":[84],"result":[85],"implies":[86],"that":[87,105],"there":[88,106],"does":[89,107],"not":[90,108],"exist":[91,109],"with":[96,123],"n-variable":[97,124],"odd":[99],"n(n":[100],"\u2265":[101,112,127],"5).":[102],"conclude":[104],"m(m":[111],"1)-resilient":[113],"n":[126],"7.":[128]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
