{"id":"https://openalex.org/W2399294179","doi":"https://doi.org/10.1109/tit.2018.2837883","title":"Full Characterization of Generalized Bent Functions as (Semi)-Bent Spaces, Their Dual, and the Gray Image","display_name":"Full Characterization of Generalized Bent Functions as (Semi)-Bent Spaces, Their Dual, and the Gray Image","publication_year":2018,"publication_date":"2018-05-17","ids":{"openalex":"https://openalex.org/W2399294179","doi":"https://doi.org/10.1109/tit.2018.2837883","mag":"2399294179"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2018.2837883","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2837883","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://repozitorij.upr.si/IzpisGradiva.php?id=9649","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007463712","display_name":"Samir Hod\u017ei\u0107","orcid":"https://orcid.org/0000-0003-1299-1502"},"institutions":[{"id":"https://openalex.org/I118905719","display_name":"University of Primorska","ror":"https://ror.org/05xefg082","country_code":"SI","type":"education","lineage":["https://openalex.org/I118905719"]}],"countries":["SI"],"is_corresponding":true,"raw_author_name":"Samir Hodzic","raw_affiliation_strings":["FAMNIT, University of Primorska, Koper, 6000, Slovenia"],"affiliations":[{"raw_affiliation_string":"FAMNIT, University of Primorska, Koper, 6000, Slovenia","institution_ids":["https://openalex.org/I118905719"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045628286","display_name":"Wilfried Meidl","orcid":null},"institutions":[{"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":["Johann Radon Institute for Computational and Applied Mathematics, OEAW, Linz, Austria"],"affiliations":[{"raw_affiliation_string":"Johann Radon Institute for Computational and Applied Mathematics, OEAW, Linz, Austria","institution_ids":["https://openalex.org/I4210158379"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039271966","display_name":"Enes Pa\u0161ali\u0107","orcid":"https://orcid.org/0000-0001-6343-8796"},"institutions":[{"id":"https://openalex.org/I118905719","display_name":"University of Primorska","ror":"https://ror.org/05xefg082","country_code":"SI","type":"education","lineage":["https://openalex.org/I118905719"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Enes Pasalic","raw_affiliation_strings":["FAMNIT, IAM, University of Primorska, Koper, Slovenia"],"affiliations":[{"raw_affiliation_string":"FAMNIT, IAM, University of Primorska, Koper, Slovenia","institution_ids":["https://openalex.org/I118905719"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007463712"],"corresponding_institution_ids":["https://openalex.org/I118905719"],"apc_list":null,"apc_paid":null,"fwci":0.3385,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.66371416,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"64","issue":"7","first_page":"5432","last_page":"5440"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9682999849319458,"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/T13779","display_name":"Cancer Mechanisms and Therapy","score":0.9672999978065491,"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":0.9504109025001526},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6040832996368408},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.595408022403717},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.5531972050666809},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5411268472671509},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.526715099811554},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5075629949569702},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5051904320716858},{"id":"https://openalex.org/keywords/bent-function","display_name":"Bent function","score":0.42913055419921875},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39271774888038635},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3638256788253784},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22408032417297363},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21361565589904785},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.20003312826156616},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16534432768821716},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.1128784716129303}],"concepts":[{"id":"https://openalex.org/C138211643","wikidata":"https://www.wikidata.org/wiki/Q675211","display_name":"Bent molecular geometry","level":2,"score":0.9504109025001526},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6040832996368408},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.595408022403717},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.5531972050666809},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5411268472671509},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.526715099811554},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5075629949569702},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5051904320716858},{"id":"https://openalex.org/C84185955","wikidata":"https://www.wikidata.org/wiki/Q4890350","display_name":"Bent function","level":3,"score":0.42913055419921875},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39271774888038635},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3638256788253784},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22408032417297363},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21361565589904785},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.20003312826156616},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16534432768821716},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.1128784716129303},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/tit.2018.2837883","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2837883","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:repozitorij.upr.si:IzpisGradiva.php?id=9649","is_oa":true,"landing_page_url":"https://repozitorij.upr.si/IzpisGradiva.php?id=9649","pdf_url":null,"source":{"id":"https://openalex.org/S4377196486","display_name":"Repository of the University of Primorsk (University of Primorska)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118905719","host_organization_name":"University of Primorska","host_organization_lineage":["https://openalex.org/I118905719"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on information theory, pp. 1-19, 2018.","raw_type":"info:eu-repo/semantics/other"},{"id":"pmh:oai:repozitorij.upr.si:IzpisGradiva.php?id=9650","is_oa":true,"landing_page_url":"https://repozitorij.upr.si/IzpisGradiva.php?id=9650","pdf_url":null,"source":{"id":"https://openalex.org/S4377196486","display_name":"Repository of the University of Primorsk (University of Primorska)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118905719","host_organization_name":"University of Primorska","host_organization_lineage":["https://openalex.org/I118905719"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISSN: 0018-9448","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1605.05713","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1605.05713","pdf_url":"https://arxiv.org/pdf/1605.05713","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":null,"raw_type":"text"},{"id":"mag:2399294179","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1605.05713v1","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.1605.05713","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1605.05713","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:repozitorij.upr.si:IzpisGradiva.php?id=9649","is_oa":true,"landing_page_url":"https://repozitorij.upr.si/IzpisGradiva.php?id=9649","pdf_url":null,"source":{"id":"https://openalex.org/S4377196486","display_name":"Repository of the University of Primorsk (University of Primorska)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118905719","host_organization_name":"University of Primorska","host_organization_lineage":["https://openalex.org/I118905719"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on information theory, pp. 1-19, 2018.","raw_type":"info:eu-repo/semantics/other"},"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/G6486294621","display_name":null,"funder_award_id":"J1-6720","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G8184292771","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G820111566","display_name":null,"funder_award_id":"P3-0384","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"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"},{"id":"https://openalex.org/F4320322554","display_name":"Javna Agencija za Raziskovalno Dejavnost RS","ror":"https://ror.org/059bp8k51"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W22007176","https://openalex.org/W564046778","https://openalex.org/W1490143729","https://openalex.org/W1498892963","https://openalex.org/W1750724710","https://openalex.org/W1874863607","https://openalex.org/W1983717725","https://openalex.org/W2016278262","https://openalex.org/W2018180443","https://openalex.org/W2032685643","https://openalex.org/W2063388923","https://openalex.org/W2068180810","https://openalex.org/W2087541534","https://openalex.org/W2087927649","https://openalex.org/W2109887866","https://openalex.org/W2118515741","https://openalex.org/W2125202015","https://openalex.org/W2154374104","https://openalex.org/W2225043332","https://openalex.org/W2285925216","https://openalex.org/W2295785816","https://openalex.org/W2337437887","https://openalex.org/W2394845742","https://openalex.org/W2465358434","https://openalex.org/W2583097765","https://openalex.org/W2600271650","https://openalex.org/W2793446615","https://openalex.org/W2951508449","https://openalex.org/W2962928091","https://openalex.org/W2963408018","https://openalex.org/W2963434092","https://openalex.org/W4214731307","https://openalex.org/W6651353164"],"related_works":["https://openalex.org/W2962859775","https://openalex.org/W2337952150","https://openalex.org/W2225043332","https://openalex.org/W2417306589","https://openalex.org/W3194727451","https://openalex.org/W2800824112","https://openalex.org/W2963408018","https://openalex.org/W2991779014","https://openalex.org/W1486768134","https://openalex.org/W2586778326","https://openalex.org/W3030837929","https://openalex.org/W3194796434","https://openalex.org/W1983717725","https://openalex.org/W117892210","https://openalex.org/W3184100626","https://openalex.org/W3185956566","https://openalex.org/W2480841162","https://openalex.org/W2892868783","https://openalex.org/W2613714965","https://openalex.org/W1894166005"],"abstract_inverted_index":{"A":[0],"natural":[1],"generalization":[2],"of":[3,9,37,45,49,62,75,84,123,135,156,198,201],"bent":[4,30,136,194],"functions":[5,10,39,112,137,140,157,178,202,212],"is":[6,26,68,78,88,128,207],"a":[7,63,85,125,129,154],"class":[8,200],"from":[11,158],"F":[12,159],"<sub":[13,160,174,216],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[14,17,22,161,164,169,175,217],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[15,162],"<sup":[16,21,163,168],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[18,165],"to":[19,166,187,192],"Z(2":[20,167],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</sup>":[23,170],")":[24],"which":[25,97,146,183],"known":[27],"as":[28,113],"generalized":[29],"(gbent)":[31],"functions.":[32,53,195],"The":[33],"construction":[34],"and":[35,105,205],"characterization":[36],"gbent":[38,64,86,111,126,211],"are":[40,180,203,213],"commonly":[41],"described":[42],"in":[43],"terms":[44],"the":[46,50,60,73,81,121],"Walsh":[47],"transforms":[48],"associated":[51],"Boolean":[52],"Using":[54],"similar":[55],"approach,":[56],"we":[57,147,151],"first":[58],"determine":[59],"dual":[61],"function":[65,87,127],"when":[66],"n":[67],"even.":[69],"Then,":[70],"depending":[71,119],"on":[72,120],"parity":[74,122],"n,":[76,124],"it":[77,206],"shown":[79],"that":[80,209],"Gray":[82],"image":[83],"(k":[89,93,130],"-":[90,94,131],"1)":[91],"or":[92,138],"2)":[95],"plateaued,":[96],"generalizes":[98],"previous":[99],"results":[100],"for":[101],"k":[102],"=":[103],"2,3,":[104],"4.":[106],"We":[107],"then":[108],"completely":[109,148],"characterize":[110],"algebraic":[114],"objects.":[115],"More":[116],"precisely,":[117],"again":[118],"1)-dimensional":[132],"affine":[133],"space":[134],"semi-bent":[139],"with":[141],"certain":[142],"interesting":[143],"additional":[144],"properties,":[145],"describe.":[149],"Finally,":[150],"also":[152],"consider":[153],"subclass":[155],"),":[171],"called":[172],"Z":[173,215],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q</sub>":[176,218],"-bent":[177],"(which":[179],"necessarily":[181],"gbent),":[182],"essentially":[184],"gives":[185],"rise":[186],"relative":[188],"difference":[189],"sets":[190],"similarly":[191],"standard":[193],"Two":[196],"examples":[197],"this":[199],"provided":[204],"demonstrated":[208],"many":[210],"not":[214],"-bent.":[219]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
