{"id":"https://openalex.org/W2885644988","doi":"https://doi.org/10.3233/fi-2018-1712","title":"A Note on the Higher\u2013order Nonlinearity of Niho Function","display_name":"A Note on the Higher\u2013order Nonlinearity of Niho Function","publication_year":2018,"publication_date":"2018-08-06","ids":{"openalex":"https://openalex.org/W2885644988","doi":"https://doi.org/10.3233/fi-2018-1712","mag":"2885644988"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2018-1712","doi":"https://doi.org/10.3233/fi-2018-1712","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2018-1712","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","ccf-c","cwts-core","ddh","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W2885644988"],"child_works_count":0,"type":"article","is_traditional":true,"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/A5060984628","display_name":"Manish Garg","orcid":"https://orcid.org/0000-0003-2066-5221","observed_orcids":["https://orcid.org/0000-0003-2066-5221"]},"institutions":[{"id":"https://openalex.org/I33552525","display_name":"LNM Institute of Information Technology","ror":"https://ror.org/03jp7rg16","country_code":"IN","type":"education","lineage":["https://openalex.org/I33552525"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Manish Garg","raw_affiliation_strings":["Department of Mathematics, The LNM Institue of Information Technology, Jaipur\u2013302031, Rajasthan, INDIA, manishiitr8@gmail.com"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The LNM Institue of Information Technology, Jaipur\u2013302031, Rajasthan, INDIA, manishiitr8@gmail.com","institution_ids":["https://openalex.org/I33552525"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060984628"],"corresponding_institution_ids":["https://openalex.org/I33552525"],"apc_list":{"value":4150,"currency":"USD","value_usd":4150},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"162","issue":"1","first_page":"37","last_page":"42"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":9.999999747378752e-05,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/higher-order-nonlinearity","display_name":"higher-order nonlinearities","score":0.8510000109672546},{"id":"https://openalex.org/keywords/boolean-functions","display_name":"Boolean functions","score":0.9259999990463257},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.6740000247955322},{"id":"https://openalex.org/keywords/trace-functions","display_name":"trace functions","score":0.8360000252723694},{"id":"https://openalex.org/keywords/finite-fields","display_name":"finite fields","score":0.6600000262260437},{"id":"https://openalex.org/keywords/proof-correction","display_name":"proof correction","score":0.39899998903274536}],"concepts":[{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.7562963962554932},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.7489532828330994},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7079551219940186},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6561609506607056},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5519555807113647},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5135088562965393},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44287580251693726},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3792847990989685},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22311460971832275},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10216078162193298},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.056899964809417725},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/fi-2018-1712","doi":"https://doi.org/10.3233/fi-2018-1712","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2018-1712","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","ccf-c","cwts-core","ddh","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1607408212","https://openalex.org/W2406357479","https://openalex.org/W1634830450","https://openalex.org/W3134842914","https://openalex.org/W7095892918","https://openalex.org/W2146112182","https://openalex.org/W4391756456","https://openalex.org/W4226189351","https://openalex.org/W2403097992","https://openalex.org/W4366317362"],"abstract_inverted_index":{"Sun":[0],"and":[1],"Wu":[2],"investigated":[3],"the":[4,11,33,50,54,61,70,77,80,90],"lower":[5,55,84],"bound":[6,56,85],"of":[7,10,29,32,38,52,57,60,83,86,89],"higher-order":[8,36,58,87],"nonlinearity":[9,37],"niho":[12,39,62,91],"Boolean":[13,63,92],"function":[14,64,93],"f(x)=Tr1n(\u03bbxd)":[15],"over":[16],"\u1d532n;":[17],"where":[18],"\u03bb\u2208F2n*,d=2n\u221212+23n\u221214\u22121":[19],"when":[20],"n":[21],"\u2261":[22],"3":[23],"mod":[24],"4":[25],"in":[26,42,69],"second":[27],"case":[28],"Theorem":[30],"3.6":[31],"paper":[34,76],"titled":[35],"functions":[40],"published":[41],"Fundamenta":[43],"Informatica":[44],"e":[45],"137":[46],"(2015)":[47],"403\u2013412.":[48],"Unfortunately,":[49],"proof":[51,82],"finding":[53],"nonlinearities":[59,88],"f(x)":[65],"is":[66],"not":[67],"correct":[68,81],"above":[71],"mentioned":[72],"paper.":[73],"In":[74],"this":[75],"author":[78],"gives":[79],"f(x).":[94]},"counts_by_year":[],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2018-08-22T00:00:00"}