{"id":"https://openalex.org/W2507564109","doi":"https://doi.org/10.1109/isit.2016.7541345","title":"On the (non-)existence of APN (n, n)-functions of algebraic degree n","display_name":"On the (non-)existence of APN (n, n)-functions of algebraic degree n","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2507564109","doi":"https://doi.org/10.1109/isit.2016.7541345","mag":"2507564109"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2016.7541345","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2016.7541345","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-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/A5035047909","display_name":"Lilya Budaghyan","orcid":null},"institutions":[{"id":"https://openalex.org/I173089394","display_name":"ITMO University","ror":"https://ror.org/04txgxn49","country_code":"RU","type":"education","lineage":["https://openalex.org/I173089394"]},{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO","RU"],"is_corresponding":true,"raw_author_name":"Lilya Budaghyan","raw_affiliation_strings":["Department of Informatics, University of Bergen, PB 7803, 5020, NORWAY","ITMO University, Saint-Petersburg, RUSSIA","Department of Informatics, University of Bergen, Bergen, NORWAY"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, PB 7803, 5020, NORWAY","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"ITMO University, Saint-Petersburg, RUSSIA","institution_ids":["https://openalex.org/I173089394"]},{"raw_affiliation_string":"Department of Informatics, University of Bergen, Bergen, NORWAY","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088687711","display_name":"Claude Carlet","orcid":"https://orcid.org/0000-0002-6118-7927"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210091279","display_name":"Universit\u00e9 Sorbonne Paris Nord","ror":"https://ror.org/0199hds37","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210091279"]},{"id":"https://openalex.org/I48825208","display_name":"Universit\u00e9 Paris 8","ror":"https://ror.org/04wez5e68","country_code":"FR","type":"education","lineage":["https://openalex.org/I48825208"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Claude Carlet","raw_affiliation_strings":["LAGA, Department of Mathematics, University of Paris 8 (and Paris 13 and CNRS), Saint-Denis cedex 02, FRANCE","Department of Mathematics, CNRS, FRANCE"],"affiliations":[{"raw_affiliation_string":"LAGA, Department of Mathematics, University of Paris 8 (and Paris 13 and CNRS), Saint-Denis cedex 02, FRANCE","institution_ids":["https://openalex.org/I48825208","https://openalex.org/I1294671590","https://openalex.org/I4210091279"]},{"raw_affiliation_string":"Department of Mathematics, CNRS, FRANCE","institution_ids":["https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026698531","display_name":"Tor Helleseth","orcid":"https://orcid.org/0000-0003-1290-3541"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Tor Helleseth","raw_affiliation_strings":["Department of Informatics, University of Bergen, PB 7803, 5020, NORWAY","Department of Informatics, University of Bergen, Bergen, NORWAY"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, PB 7803, 5020, NORWAY","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"Department of Informatics, University of Bergen, Bergen, NORWAY","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100400586","display_name":"Nian Li","orcid":"https://orcid.org/0000-0003-4913-7844"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Nian Li","raw_affiliation_strings":["Department of Informatics, University of Bergen, PB 7803, 5020, NORWAY","Department of Informatics, University of Bergen, Bergen, NORWAY"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, PB 7803, 5020, NORWAY","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"Department of Informatics, University of Bergen, Bergen, NORWAY","institution_ids":["https://openalex.org/I4432739"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5035047909"],"corresponding_institution_ids":["https://openalex.org/I173089394","https://openalex.org/I4432739"],"apc_list":null,"apc_paid":null,"fwci":0.4443,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.79186047,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"480","last_page":"484"},"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":0.9977999925613403,"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":0.9958999752998352,"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/algebraic-number","display_name":"Algebraic number","score":0.4961720407009125},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4336678087711334},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3423658013343811},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32883942127227783},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2730448246002197},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08434247970581055},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.07488560676574707}],"concepts":[{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4961720407009125},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4336678087711334},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3423658013343811},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32883942127227783},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2730448246002197},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08434247970581055},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.07488560676574707},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2016.7541345","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2016.7541345","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W37385681","https://openalex.org/W567095041","https://openalex.org/W1498892963","https://openalex.org/W1528065150","https://openalex.org/W1571322537","https://openalex.org/W1587687098","https://openalex.org/W1629301835","https://openalex.org/W1964723977","https://openalex.org/W2020301329","https://openalex.org/W2024156986","https://openalex.org/W2024729203","https://openalex.org/W2048462185","https://openalex.org/W2082143349","https://openalex.org/W2100083939","https://openalex.org/W2114121479","https://openalex.org/W2173356534","https://openalex.org/W4211127378","https://openalex.org/W6634242673"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052","https://openalex.org/W4402327032","https://openalex.org/W2382290278"],"abstract_inverted_index":{"We":[0,22,37],"study":[1],"the":[2,34,50,63],"problem":[3],"of":[4,6,9,28,33,49,84],"existence":[5],"APN":[7,52],"functions":[8,25,53],"algebraic":[10],"degree":[11],"n":[12],"over":[13,55],"F":[14,54,56,85],"<sub":[15,18,57,60],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[16,19,58,61,67,70,73],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[17,59],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sub>":[20,62],".":[21],"characterize":[23],"such":[24],"by":[26],"means":[27],"derivatives":[29],"and":[30,80],"power":[31],"moments":[32],"Walsh":[35],"transform.":[36],"deduce":[38],"some":[39],"non-existence":[40],"results":[41,90],"which":[42],"mean,":[43],"in":[44,86,91],"particular,":[45],"that":[46],"for":[47],"most":[48],"known":[51],"function":[64],"x":[65],"<sup":[66,69,72],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[68],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[71],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">-1</sup>":[74],"+":[75],"F(x)":[76],"is":[77],"not":[78],"APN,":[79],"changing":[81],"a":[82,87],"value":[83],"single":[88],"point":[89],"non-APN":[92],"functions.":[93]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}