{"id":"https://openalex.org/W4399309658","doi":"https://doi.org/10.3934/amc.2024025","title":"On vectorial functions mapping strict affine subspaces of their domain into strict affine subspaces of their co-domain, and the strong D-property","display_name":"On vectorial functions mapping strict affine subspaces of their domain into strict affine subspaces of their co-domain, and the strong D-property","publication_year":2024,"publication_date":"2024-06-03","ids":{"openalex":"https://openalex.org/W4399309658","doi":"https://doi.org/10.3934/amc.2024025"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2024025","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2024025","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=665d8bb0ce1f3501b2a85db9","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/data/article/export-pdf?id=665d8bb0ce1f3501b2a85db9","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088687711","display_name":"Claude Carlet","orcid":"https://orcid.org/0000-0002-6118-7927"},"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"]},{"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","NO"],"is_corresponding":true,"raw_author_name":"Claude Carlet","raw_affiliation_strings":["University of Bergen, Bergen, Norway","University of Paris 8, Saint-Denis, France"],"affiliations":[{"raw_affiliation_string":"University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"University of Paris 8, Saint-Denis, France","institution_ids":["https://openalex.org/I48825208"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060121292","display_name":"Enrico Piccione","orcid":"https://orcid.org/0000-0002-1929-7700"},"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":"Enrico Piccione","raw_affiliation_strings":["University of Bergen, Bergen, Norway"],"affiliations":[{"raw_affiliation_string":"University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5088687711"],"corresponding_institution_ids":["https://openalex.org/I4432739","https://openalex.org/I48825208"],"apc_list":null,"apc_paid":null,"fwci":0.3862,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.63714776,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"19","issue":"3","first_page":"793","last_page":"828"},"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9980999827384949,"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"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/linear-subspace","display_name":"Linear subspace","score":0.9200104475021362},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9146717190742493},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.8757501840591431},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6887454986572266},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.6718800067901611},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5444411635398865},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3236958980560303},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32366710901260376},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23101481795310974}],"concepts":[{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.9200104475021362},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9146717190742493},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.8757501840591431},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6887454986572266},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6718800067901611},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5444411635398865},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3236958980560303},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32366710901260376},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23101481795310974},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2024025","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2024025","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=665d8bb0ce1f3501b2a85db9","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2024025","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2024025","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=665d8bb0ce1f3501b2a85db9","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.47999998927116394,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4399309658.pdf"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1567788290","https://openalex.org/W1858314666","https://openalex.org/W1935580934","https://openalex.org/W1971990650","https://openalex.org/W1976677460","https://openalex.org/W2024900297","https://openalex.org/W2025323123","https://openalex.org/W2050972703","https://openalex.org/W2060440857","https://openalex.org/W2072556008","https://openalex.org/W2102294760","https://openalex.org/W2759739548","https://openalex.org/W2761574822","https://openalex.org/W2790824722","https://openalex.org/W2912272895","https://openalex.org/W2914450592","https://openalex.org/W3015255432","https://openalex.org/W3210873239","https://openalex.org/W4205482204","https://openalex.org/W4220862074","https://openalex.org/W4248135912","https://openalex.org/W4313166192","https://openalex.org/W4320727006"],"related_works":["https://openalex.org/W2391321755","https://openalex.org/W2949110394","https://openalex.org/W2896134808","https://openalex.org/W4289378085","https://openalex.org/W2071055957","https://openalex.org/W140666874","https://openalex.org/W2022655107","https://openalex.org/W1970586498","https://openalex.org/W2149321764","https://openalex.org/W4295628982"],"abstract_inverted_index":{"Given":[0],"three":[1],"positive":[2],"integers":[3],"$":[4,6,8,16,19,21,25,30,32,35,41,43,46,53,56,58,62,71,73,115,119,121,123,127,129,131,133,140,142,164,167,171,173,185,188,201,204,242,244,275,277,323,331,334,338,340,344,346,348,358,360,385,389,402,404,406],"n<N":[5],"and":[7,44,82,120,139,217,229,237,293,357,405],"M":[9,116],"$,":[10,169],"we":[11,83,98,194,230,282,300,372,392],"studied":[12],"those":[13],"vectorial":[14],"Boolean":[15],"(N,M)":[17],"$-functions":[18,55,166,187,203,333],"\\mathcal{F}":[20,63,72,122],"which":[22],"mapped":[23],"an":[24,34,362],"n":[26,49,386],"$-dimensional":[27,37],"affine":[28,38],"space":[29,39],"A":[31,172],"into":[33],"m":[36,47],"where":[40,130,170,345],"m<M":[42],"possibly":[45],"=":[48,117,336,342,387],"$.":[50,64,190,206,408],"This":[51],"provided":[52,373],"(n,m)":[54],"\\mathcal{F}_A":[57,189],"as":[59,308,327],"restrictions":[60,329],"of":[61,70,103,124,150,158,162,182,211,226,268,297,320,330,354],"We":[65,109,153,207,253,310],"showed":[66,99],"that":[67,85,100,155,232,264,302,378],"the":[68,101,104,113,125,156,160,180,196,233,250,265,269,288,295,305,328],"nonlinearity":[69,102],"must":[74],"not":[75,381],"be":[76,107],"too":[77],"large":[78],"for":[79,200,214,274],"allowing":[80],"this,":[81],"observed":[84,154],"if":[86],"it":[87,91,222,303],"was":[88,92,134,143,174,177,349,361],"zero,":[89],"then":[90,110,311],"always":[93],"possible.":[94],"In":[95],"this":[96,192,212,298],"case,":[97],"restriction":[105],"may":[106],"large.":[108],"focused":[111],"on":[112,287,294,369,401],"case":[114],"N":[118,243,276],"form":[126],"\\psi(\\mathcal{G}(x))":[128,337],"\\mathcal{G}":[132,205,359,407],"almost":[135],"perfect":[136],"nonlinear":[137],"(APN)":[138],"\\psi":[141,347,403],"a":[144,148,175,209,258,284,352,366],"linear":[145,350],"function":[146,236,272],"with":[147,351],"kernel":[149,353],"dimension":[151,241,355,384],"1.":[152],"problem":[157,181],"determining":[159],"D-property":[161,198,267,307],"APN":[163,184,235,271,290,363,382],"(N-1,N)":[165],"\\mathcal{G}_A":[168],"hyperplane,":[176],"related":[178],"to":[179,315],"constructing":[183],"(N-1,N-1)":[186,324],"For":[191],"reason,":[193],"introduce":[195],"strong":[197,251,266,306],"defined":[199],"(N,N)":[202,332],"gave":[208,283],"characterization":[210],"property":[213],"crooked":[215],"functions":[216],"their":[218,227],"compositional":[219],"inverse":[220,239],"(if":[221],"existed)":[223],"by":[224,397],"means":[225],"ortho-derivatives,":[228],"proved":[231,255],"Gold":[234,270],"its":[238],"in":[240,256,262,383],"odd":[245],"big":[246,279],"enough":[247],"both":[248],"had":[249],"D-property.":[252],"also":[254],"simpler":[257],"way":[259],"than":[260],"Taniguchi":[261],"2023":[263],"holds":[273],"even":[278],"enough.":[280],"Then,":[281,391],"partial":[285],"result":[286],"Dobbertin":[289],"power":[291],"function,":[292],"basis":[296],"result,":[299],"conjectured":[301],"has":[304],"well.":[309],"moved":[312],"our":[313,394],"focus":[314],"two":[316],"known":[317],"infinite":[318],"families":[319],"differentially":[321],"4-uniform":[322],"$-permutations":[325],"constructed":[326],"\\mathcal{F}(x)":[335,341],"or":[339],"\\psi(\\mathcal{G}(x))+x":[343],"1":[356],"permutation.":[364],"After":[365],"deeper":[367],"investigation":[368],"these":[370],"classes,":[371],"proofs":[374],"(which":[375],"were":[376],"missing)":[377],"they":[379],"are":[380],"N-1":[388],"even.":[390],"presented":[393],"own":[395],"construction":[396],"relaxing":[398],"some":[399],"hypotheses":[400]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}