{"id":"https://openalex.org/W3021083864","doi":"https://doi.org/10.1142/s0129054120500161","title":"Monomial Generalized Almost Perfect Nonlinear Functions","display_name":"Monomial Generalized Almost Perfect Nonlinear Functions","publication_year":2020,"publication_date":"2020-04-01","ids":{"openalex":"https://openalex.org/W3021083864","doi":"https://doi.org/10.1142/s0129054120500161","mag":"3021083864"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054120500161","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054120500161","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/A5102864620","display_name":"Masamichi Kuroda","orcid":"https://orcid.org/0000-0001-8980-0431"},"institutions":[{"id":"https://openalex.org/I27551014","display_name":"Nippon Bunri University","ror":"https://ror.org/02wp4vw89","country_code":"JP","type":"education","lineage":["https://openalex.org/I27551014"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Masamichi Kuroda","raw_affiliation_strings":["Faculty of Engineering, Nippon Bunri University, Oita, Japan"],"raw_orcid":"https://orcid.org/0000-0001-8980-0431","affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Nippon Bunri University, Oita, Japan","institution_ids":["https://openalex.org/I27551014"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102864620"],"corresponding_institution_ids":["https://openalex.org/I27551014"],"apc_list":null,"apc_paid":null,"fwci":0.68,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.76138792,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"31","issue":"03","first_page":"411","last_page":"419"},"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":0.9814000129699707,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.98089998960495,"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/monomial","display_name":"Monomial","score":0.9448140859603882},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8225442171096802},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7767273187637329},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.7212476134300232},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6417436599731445},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5343291759490967},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.49418333172798157},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.44538018107414246},{"id":"https://openalex.org/keywords/algebraic-structure","display_name":"Algebraic structure","score":0.41593432426452637},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4041939377784729},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34357571601867676},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33586013317108154},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16936644911766052}],"concepts":[{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.9448140859603882},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8225442171096802},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7767273187637329},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.7212476134300232},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6417436599731445},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5343291759490967},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.49418333172798157},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.44538018107414246},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.41593432426452637},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4041939377784729},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34357571601867676},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33586013317108154},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16936644911766052},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054120500161","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054120500161","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1528065150","https://openalex.org/W1531334709","https://openalex.org/W1554932142","https://openalex.org/W1562191210","https://openalex.org/W1571322537","https://openalex.org/W1963623275","https://openalex.org/W2015894712","https://openalex.org/W2021875115","https://openalex.org/W2024483577","https://openalex.org/W2048462185","https://openalex.org/W2048606081","https://openalex.org/W2052178764","https://openalex.org/W2068656449","https://openalex.org/W2087896741","https://openalex.org/W2481217652","https://openalex.org/W2951489851","https://openalex.org/W2963192837","https://openalex.org/W3101286711","https://openalex.org/W3104021212","https://openalex.org/W4213002315"],"related_works":["https://openalex.org/W51281323","https://openalex.org/W38312493","https://openalex.org/W7978484","https://openalex.org/W833627","https://openalex.org/W14429072","https://openalex.org/W31094085","https://openalex.org/W3427452","https://openalex.org/W24365269","https://openalex.org/W13616303","https://openalex.org/W18299066"],"abstract_inverted_index":{"Generalized":[0],"almost":[1,16],"perfect":[2,17],"nonlinear":[3,18],"(GAPN)":[4],"functions":[5,20,33,45,53,76],"were":[6],"defined":[7],"to":[8],"satisfy":[9],"some":[10],"generalizations":[11],"of":[12,15,29,65,73],"basic":[13],"properties":[14],"(APN)":[19],"for":[21,46],"even":[22,30],"characteristic.":[23,48,67],"In":[24,38],"particular,":[25],"on":[26,61],"finite":[27,63],"fields":[28],"characteristic,":[31],"GAPN":[32,44,52],"coincide":[34],"with":[35],"APN":[36,75],"functions.":[37],"this":[39],"paper,":[40],"we":[41,69],"study":[42],"monomial":[43,51],"odd":[47,66],"We":[49],"give":[50,78],"whose":[54],"algebraic":[55],"degree":[56],"are":[57],"maximum":[58],"or":[59],"minimum":[60],"a":[62,71],"field":[64],"Moreover,":[68],"define":[70],"generalization":[72],"exceptional":[74],"and":[77],"typical":[79],"examples.":[80]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2}],"updated_date":"2026-05-09T13:55:54.758798","created_date":"2025-10-10T00:00:00"}
