{"id":"https://openalex.org/W6968784825","doi":"https://doi.org/10.5281/zenodo.16752428","title":"Millions of inequivalent quadratic APN functions in eight variables","display_name":"Millions of inequivalent quadratic APN functions in eight variables","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W6968784825","doi":"https://doi.org/10.5281/zenodo.16752428"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.16752428","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.16752428","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dataset"},"type":"dataset","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.16752428","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Beierle, Christof","orcid":"https://orcid.org/0000-0002-5558-0722"},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Beierle, Christof","raw_affiliation_strings":["Ruhr University Bochum"],"raw_orcid":"https://orcid.org/0000-0002-5558-0722","affiliations":[{"raw_affiliation_string":"Ruhr University Bochum","institution_ids":["https://openalex.org/I904495901"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Langevin, Philippe","orcid":"https://orcid.org/0000-0002-3661-048X"},"institutions":[{"id":"https://openalex.org/I143002897","display_name":"Universit\u00e9 de Toulon","ror":"https://ror.org/02m9kbe37","country_code":"FR","type":"education","lineage":["https://openalex.org/I143002897"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Langevin, Philippe","raw_affiliation_strings":["Universit\u00e9 de Toulon"],"raw_orcid":"https://orcid.org/0000-0002-3661-048X","affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Toulon","institution_ids":["https://openalex.org/I143002897"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Leander, Gregor","orcid":"https://orcid.org/0000-0002-2579-8587"},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Leander, Gregor","raw_affiliation_strings":["Ruhr University Bochum"],"raw_orcid":"https://orcid.org/0000-0002-2579-8587","affiliations":[{"raw_affiliation_string":"Ruhr University Bochum","institution_ids":["https://openalex.org/I904495901"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Polujan, Alexandr","orcid":"https://orcid.org/0000-0002-0461-4793"},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke-Universit\u00e4t Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Polujan, Alexandr","raw_affiliation_strings":["Otto-von-Guericke University Magdeburg"],"raw_orcid":"https://orcid.org/0000-0002-0461-4793","affiliations":[{"raw_affiliation_string":"Otto-von-Guericke University Magdeburg","institution_ids":["https://openalex.org/I95793202"]}]},{"author_position":"last","author":{"id":null,"display_name":"Rasoolzadeh, Shahram","orcid":"https://orcid.org/0000-0001-6848-2227"},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Rasoolzadeh, Shahram","raw_affiliation_strings":["Ruhr University Bochum"],"raw_orcid":"https://orcid.org/0000-0001-6848-2227","affiliations":[{"raw_affiliation_string":"Ruhr University Bochum","institution_ids":["https://openalex.org/I904495901"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9269999861717224,"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":0.9269999861717224,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.006099999882280827,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.005900000222027302,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/quadratic-equation","display_name":"Quadratic equation","score":0.7692999839782715},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6297000050544739},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.4950000047683716},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.4903999865055084},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4625000059604645},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.3944000005722046},{"id":"https://openalex.org/keywords/quadratic-model","display_name":"Quadratic model","score":0.3896999955177307}],"concepts":[{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.7692999839782715},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6319000124931335},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6297000050544739},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.4950000047683716},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.4903999865055084},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4625000059604645},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.3944000005722046},{"id":"https://openalex.org/C2983524802","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic model","level":3,"score":0.3896999955177307},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3837999999523163},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.351500004529953},{"id":"https://openalex.org/C12817185","wikidata":"https://www.wikidata.org/wiki/Q878259","display_name":"Quadratic residue","level":2,"score":0.34450000524520874},{"id":"https://openalex.org/C80695182","wikidata":"https://www.wikidata.org/wiki/Q864134","display_name":"Binary quadratic form","level":4,"score":0.3384000062942505},{"id":"https://openalex.org/C177179195","wikidata":"https://www.wikidata.org/wiki/Q7268372","display_name":"Quadratic unconstrained binary optimization","level":4,"score":0.33320000767707825},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C21440807","wikidata":"https://www.wikidata.org/wiki/Q4968811","display_name":"Isotropic quadratic form","level":5,"score":0.3061000108718872},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3057999908924103},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29679998755455017},{"id":"https://openalex.org/C152022596","wikidata":"https://www.wikidata.org/wiki/Q7268361","display_name":"Quadratic form (statistics)","level":2,"score":0.28850001096725464},{"id":"https://openalex.org/C2778433361","wikidata":"https://www.wikidata.org/wiki/Q7268358","display_name":"Quadratic differential","level":3,"score":0.2849000096321106}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.5281/zenodo.16752428","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.16752428","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Dataset"}],"best_oa_location":{"id":"doi:10.5281/zenodo.16752428","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.16752428","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dataset"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"dataset":[1],"contains":[2,70],"the":[3,7,22,51,71,107,113,117,124,129,133,139,147],"look-up":[4,72],"tables":[5,73],"of":[6,39,74],"new":[8,77],"3,775,599":[9,76],"inequivalent":[10,40],"quadratic":[11,41,78,86,101],"APN":[12,42,79,87,102,109,119,126,135,141,149],"functions":[13,43,88,103,110,120,127,136,142,150],"in":[14,25,44,89,105,122,144,152],"dimension":[15],"eight":[16,45,90],"(up":[17,94],"to":[18,82,95],"EA-equivalence)":[19],"found":[20],"by":[21,112],"approaches":[23],"described":[24],"our":[26,83],"work":[27],"[C.":[28],"Beierle,":[29],"P.":[30],"Langevin,":[31],"G.":[32],"Leander,":[33],"A.":[34],"Polujan,":[35],"S.":[36],"Rasoolzadeh.":[37],"Millions":[38],"variables.":[46],"arXiv:2508.04644":[47],"(2025)],":[48],"presented":[49,121,143],"at":[50],"10th":[52],"International":[53],"Workshop":[54],"on":[55],"Boolean":[56],"Functions":[57],"and":[58,146],"their":[59],"Applications":[60],"(BFA),":[61],"September":[62],"1-5,":[63],"2025,":[64],"Larnaca,":[65],"Cyprus.":[66],"The":[67,99],"file":[68],"new_apns.txt":[69],"these":[75],"functions.":[80],"Prior":[81],"work,":[84],"32,892":[85],"variables":[91],"are":[92],"known":[93],"EA-equivalence).":[96],"Those":[97],"are:":[98],"22":[100],"listed":[104],"[EP09],":[106],"8,157":[108],"constructed":[111,151],"QAM":[114],"method":[115],"[YWL14],":[116],"10":[118],"[WTG13],":[123],"two":[125],"from":[128,137],"Taniguchi":[130],"family":[131],"[Tan19],":[132],"12,921":[134],"[BL22],":[138],"5,412":[140],"[YP22],":[145],"6,368":[148],"[BLP22].":[153]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-10-10T00:00:00"}