{"id":"https://openalex.org/W2140166183","doi":"https://doi.org/10.1109/tit.2016.2586081","title":"There Are Infinitely Many Bent Functions for Which the Dual Is Not Bent","display_name":"There Are Infinitely Many Bent Functions for Which the Dual Is Not Bent","publication_year":2016,"publication_date":"2016-06-29","ids":{"openalex":"https://openalex.org/W2140166183","doi":"https://doi.org/10.1109/tit.2016.2586081","mag":"2140166183"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2016.2586081","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2586081","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1511.02505","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002859392","display_name":"Ay\u00e7a \u00c7e\u015fmelio\u011flu","orcid":"https://orcid.org/0000-0001-5049-9135"},"institutions":[{"id":"https://openalex.org/I42317466","display_name":"Alt\u0131nba\u015f University","ror":"https://ror.org/0145w8333","country_code":"TR","type":"education","lineage":["https://openalex.org/I42317466"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Ayca Cesmelioglu","raw_affiliation_strings":["School of Engineering and Natural Sciences, \u0130stanbul Kemerburgaz University, \u0130stanbul, Turkey","[School of Engineering and Natural Sciences, \u0130stanbul Kemerburgaz University, \u0130stanbul, Turkey]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering and Natural Sciences, \u0130stanbul Kemerburgaz University, \u0130stanbul, Turkey","institution_ids":["https://openalex.org/I42317466"]},{"raw_affiliation_string":"[School of Engineering and Natural Sciences, \u0130stanbul Kemerburgaz University, \u0130stanbul, Turkey]","institution_ids":["https://openalex.org/I42317466"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045628286","display_name":"Wilfried Meidl","orcid":null},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"government","lineage":["https://openalex.org/I138211613"]},{"id":"https://openalex.org/I4210158379","display_name":"Johann Radon Institute for Computational and Applied Mathematics","ror":"https://ror.org/05a94k872","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Wilfried Meidl","raw_affiliation_strings":["Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria"],"raw_orcid":"https://orcid.org/0000-0002-6270-7605","affiliations":[{"raw_affiliation_string":"Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria","institution_ids":["https://openalex.org/I4210158379","https://openalex.org/I138211613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013787536","display_name":"Alexander Pott","orcid":"https://orcid.org/0000-0002-1125-1003"},"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":"Alexander Pott","raw_affiliation_strings":["Faculty of Mathematics, Otto-von-Guericke University, Magdeburg, Germany","FACULTY OF MATHEMATICS; OTTO-VON-GUERICKE UNIVERSITY; MAGDEBURG GERMANY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Otto-von-Guericke University, Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]},{"raw_affiliation_string":"FACULTY OF MATHEMATICS; OTTO-VON-GUERICKE UNIVERSITY; MAGDEBURG GERMANY","institution_ids":["https://openalex.org/I95793202"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4416,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.77615261,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"62","issue":"9","first_page":"5204","last_page":"5208"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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/T12505","display_name":"Peptidase Inhibition and Analysis","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2730","display_name":"Oncology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T13779","display_name":"Cancer Mechanisms and Therapy","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/2734","display_name":"Pathology and Forensic Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bent-molecular-geometry","display_name":"Bent molecular geometry","score":0.9864661693572998},{"id":"https://openalex.org/keywords/bent-function","display_name":"Bent function","score":0.8298330307006836},{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.7654474973678589},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49105048179626465},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.48411428928375244},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46253469586372375},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4465729594230652},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.34864211082458496},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.08178165555000305},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.059388160705566406},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.05401432514190674}],"concepts":[{"id":"https://openalex.org/C138211643","wikidata":"https://www.wikidata.org/wiki/Q675211","display_name":"Bent molecular geometry","level":2,"score":0.9864661693572998},{"id":"https://openalex.org/C84185955","wikidata":"https://www.wikidata.org/wiki/Q4890350","display_name":"Bent function","level":3,"score":0.8298330307006836},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.7654474973678589},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49105048179626465},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.48411428928375244},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46253469586372375},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4465729594230652},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.34864211082458496},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.08178165555000305},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.059388160705566406},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.05401432514190674},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2016.2586081","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2586081","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1511.02505","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.02505","pdf_url":"https://arxiv.org/pdf/1511.02505","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2140166183","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1511.02505v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1511.02505","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1511.02505","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1511.02505","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.02505","pdf_url":"https://arxiv.org/pdf/1511.02505","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1525001178","display_name":null,"funder_award_id":"M 1767-N26","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G8632160903","display_name":"Functions with special Walsh transforms","funder_award_id":"M 1767","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2140166183.pdf","grobid_xml":"https://content.openalex.org/works/W2140166183.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1511108167","https://openalex.org/W1607868314","https://openalex.org/W2003667685","https://openalex.org/W2032685643","https://openalex.org/W2032738142","https://openalex.org/W2064093194","https://openalex.org/W2077153543","https://openalex.org/W2079976070","https://openalex.org/W2090432705","https://openalex.org/W2098933212","https://openalex.org/W2110003303","https://openalex.org/W2139878845","https://openalex.org/W2162960469","https://openalex.org/W2286164450","https://openalex.org/W6728837508"],"related_works":["https://openalex.org/W2964154379","https://openalex.org/W2079976070","https://openalex.org/W3042755559","https://openalex.org/W2949764448","https://openalex.org/W2963714594","https://openalex.org/W1790462938","https://openalex.org/W2285855434","https://openalex.org/W2077153543","https://openalex.org/W2496503903","https://openalex.org/W2071445534","https://openalex.org/W2543724128","https://openalex.org/W2388086703","https://openalex.org/W2577077128","https://openalex.org/W1621393510","https://openalex.org/W2036675812","https://openalex.org/W977779969","https://openalex.org/W2363459825","https://openalex.org/W2892868783","https://openalex.org/W2501835529","https://openalex.org/W3194727451"],"abstract_inverted_index":{"Bent":[0],"functions":[1,26,58,65,83,96,120,135],"can":[2,130],"be":[3],"classified":[4],"into":[5],"regular":[6,10,13,18,24,46,56,81],"bent":[7,14,19,25,36,47,57,64,82,90,119],"functions,":[8,15],"weakly":[9,23],"but":[11],"not":[12,42,89],"and":[16,22,121],"non-weakly":[17,45,55,80],"functions.":[20,37,48,98],"Regular":[21],"always":[27],"appear":[28],"in":[29],"pairs,":[30],"since":[31],"their":[32],"duals":[33],"are":[34],"also":[35,71],"In":[38,73],"general,":[39],"this":[40,74],"does":[41],"apply":[43],"to":[44],"However,":[49],"the":[50,68,76,86,115,123],"first":[51,77],"known":[52],"construction":[53,78,124],"of":[54,79,118,139],"by":[59,125],"\u00c7e\u015fmelio\u011flu":[60,126],"et":[61,127],"al.":[62],"yields":[63],"for":[66,84],"which":[67,85],"dual":[69,87],"is":[70,88,91,143],"bent.":[72],"paper,":[75],"presented.":[92],"We":[93,110],"call":[94],"such":[95],"non-dual-bent":[97,134,141],"Until":[99],"now,":[100],"only":[101],"sporadic":[102],"examples":[103],"found":[104],"via":[105],"computer":[106],"search":[107],"were":[108],"known.":[109,144],"then":[111],"show":[112],"that":[113],"with":[114,122],"direct":[116],"sum":[117],"al.,":[128],"one":[129,137],"obtain":[131],"infinitely":[132],"many":[133],"once":[136],"example":[138],"a":[140],"function":[142]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}