{"id":"https://openalex.org/W3209745082","doi":"https://doi.org/10.3934/amc.2021048","title":"Vandermonde sets, hyperovals and Niho bent functions","display_name":"Vandermonde sets, hyperovals and Niho bent functions","publication_year":2021,"publication_date":"2021-10-27","ids":{"openalex":"https://openalex.org/W3209745082","doi":"https://doi.org/10.3934/amc.2021048","mag":"3209745082"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2021048","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2021048","pdf_url":null,"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":null,"license_id":null,"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://doi.org/10.3934/amc.2021048","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019241201","display_name":"Kanat Abdukhalikov","orcid":"https://orcid.org/0000-0003-0670-1361"},"institutions":[{"id":"https://openalex.org/I201726411","display_name":"United Arab Emirates University","ror":"https://ror.org/01km6p862","country_code":"AE","type":"education","lineage":["https://openalex.org/I201726411"]}],"countries":["AE"],"is_corresponding":true,"raw_author_name":"Kanat Abdukhalikov","raw_affiliation_strings":["UAE University, PO Box 15551, Al Ain, United Arab Emirates"],"affiliations":[{"raw_affiliation_string":"UAE University, PO Box 15551, Al Ain, United Arab Emirates","institution_ids":["https://openalex.org/I201726411"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030051451","display_name":"Duy Ho","orcid":"https://orcid.org/0000-0002-1593-8187"},"institutions":[{"id":"https://openalex.org/I201726411","display_name":"United Arab Emirates University","ror":"https://ror.org/01km6p862","country_code":"AE","type":"education","lineage":["https://openalex.org/I201726411"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Duy Ho","raw_affiliation_strings":["UAE University, PO Box 15551, Al Ain, United Arab Emirates"],"affiliations":[{"raw_affiliation_string":"UAE University, PO Box 15551, Al Ain, United Arab Emirates","institution_ids":["https://openalex.org/I201726411"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019241201"],"corresponding_institution_ids":["https://openalex.org/I201726411"],"apc_list":null,"apc_paid":null,"fwci":0.2796,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.64965926,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"17","issue":"5","first_page":"1235","last_page":"1250"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.9962999820709229,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/vandermonde-matrix","display_name":"Vandermonde matrix","score":0.9582498669624329},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8755354285240173},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6059390902519226},{"id":"https://openalex.org/keywords/bent-molecular-geometry","display_name":"Bent molecular geometry","score":0.5355958938598633},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4603675603866577},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4228897988796234},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08086323738098145},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.053174346685409546}],"concepts":[{"id":"https://openalex.org/C55294529","wikidata":"https://www.wikidata.org/wiki/Q579544","display_name":"Vandermonde matrix","level":3,"score":0.9582498669624329},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8755354285240173},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6059390902519226},{"id":"https://openalex.org/C138211643","wikidata":"https://www.wikidata.org/wiki/Q675211","display_name":"Bent molecular geometry","level":2,"score":0.5355958938598633},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4603675603866577},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4228897988796234},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08086323738098145},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.053174346685409546},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2021048","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2021048","pdf_url":null,"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":null,"license_id":null,"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.2021048","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2021048","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W59572088","https://openalex.org/W1471103927","https://openalex.org/W1490235452","https://openalex.org/W1543840521","https://openalex.org/W1750218553","https://openalex.org/W1994041682","https://openalex.org/W2022152781","https://openalex.org/W2022697667","https://openalex.org/W2023441450","https://openalex.org/W2077816506","https://openalex.org/W2086996205","https://openalex.org/W2100677873","https://openalex.org/W2105663755","https://openalex.org/W2286164450","https://openalex.org/W2519197786","https://openalex.org/W2578348831","https://openalex.org/W2913448593","https://openalex.org/W2982492865","https://openalex.org/W3002053069","https://openalex.org/W3021675569","https://openalex.org/W3100794440","https://openalex.org/W3160584957","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2394313973","https://openalex.org/W1258664604","https://openalex.org/W4285223790","https://openalex.org/W2952052090","https://openalex.org/W4293585078","https://openalex.org/W2389636997","https://openalex.org/W2349018871","https://openalex.org/W2135355720","https://openalex.org/W2080915594"],"abstract_inverted_index":{"<p":[0],"style='text-indent:20px;'>We":[1],"consider":[2],"relationships":[3],"between":[4],"Vandermonde":[5,11,16,29],"sets":[6,17],"and":[7,24,55],"hyperovals.":[8,20,50],"Hyperovals":[9],"are":[10,18],"sets,":[12],"but":[13],"in":[14,35,63],"general,":[15],"not":[19],"We":[21,85],"give":[22,53],"necessary":[23,54],"sufficient":[25,56],"conditions":[26,57],"for":[27,46,58,80],"a":[28,33],"set":[30],"to":[31,91],"be":[32,72],"hyperoval":[34],"terms":[36,64],"of":[37,49,61,65,77],"power":[38],"sums.":[39],"Therefore,":[40],"we":[41,52],"provide":[42],"purely":[43],"algebraic":[44],"criteria":[45],"the":[47,59],"existence":[48,60],"Furthermore,":[51],"hyperovals":[62],"<inline-formula><tex-math":[66,81],"id=\"M1\">\\begin{document}$":[67],"g":[68],"$\\end{document}</tex-math></inline-formula>-functions,":[69],"which":[70],"can":[71],"considered":[73],"as":[74],"an":[75],"analog":[76],"Glynn's":[78],"Theorem":[79],"id=\"M2\">\\begin{document}$":[82],"o":[83],"$\\end{document}</tex-math></inline-formula>-polynomials.":[84],"also":[86],"get":[87],"some":[88],"important":[89],"applications":[90],"Niho":[92],"bent":[93],"functions.":[94]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2021-11-08T00:00:00"}
