{"id":"https://openalex.org/W2970864062","doi":"https://doi.org/10.1007/s10623-019-00712-y","title":"Cubic bent functions outside the completed Maiorana-McFarland class","display_name":"Cubic bent functions outside the completed Maiorana-McFarland class","publication_year":2020,"publication_date":"2020-02-13","ids":{"openalex":"https://openalex.org/W2970864062","doi":"https://doi.org/10.1007/s10623-019-00712-y","mag":"2970864062"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-019-00712-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-019-00712-y","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/s10623-019-00712-y","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Alexandr A. Polujan","orcid":"https://orcid.org/0000-0002-0461-4793"},"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":"Alexandr A. Polujan","raw_affiliation_strings":["Otto von Guericke University, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany"],"raw_orcid":"https://orcid.org/0000-0002-0461-4793","affiliations":[{"raw_affiliation_string":"Otto von Guericke University, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]}]},{"author_position":"last","author":{"id":null,"display_name":"Alexander Pott","orcid":null},"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":["Otto von Guericke University, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Otto von Guericke University, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.2187,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.83559394,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"88","issue":"9","first_page":"1701","last_page":"1722"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9923999905586243,"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":0.9923999905586243,"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/T10849","display_name":"Finite Group Theory Research","score":0.002400000113993883,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.0005000000237487257,"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/bent-molecular-geometry","display_name":"Bent molecular geometry","score":0.8691999912261963},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.7630000114440918},{"id":"https://openalex.org/keywords/bent-function","display_name":"Bent function","score":0.7020000219345093},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.680400013923645},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.5885000228881836},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4025999903678894}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8899999856948853},{"id":"https://openalex.org/C138211643","wikidata":"https://www.wikidata.org/wiki/Q675211","display_name":"Bent molecular geometry","level":2,"score":0.8691999912261963},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7630000114440918},{"id":"https://openalex.org/C84185955","wikidata":"https://www.wikidata.org/wiki/Q4890350","display_name":"Bent function","level":3,"score":0.7020000219345093},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.680400013923645},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5885000228881836},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.579200029373169},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4162999987602234},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4025999903678894},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.3824000060558319},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36410000920295715},{"id":"https://openalex.org/C154610627","wikidata":"https://www.wikidata.org/wiki/Q382491","display_name":"Affine plane (incidence geometry)","level":3,"score":0.3596000075340271},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C65559279","wikidata":"https://www.wikidata.org/wiki/Q16667694","display_name":"Cubic function","level":2,"score":0.25440001487731934}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10623-019-00712-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-019-00712-y","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1908.11271","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1908.11271","pdf_url":"https://arxiv.org/pdf/1908.11271","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"}],"best_oa_location":{"id":"doi:10.1007/s10623-019-00712-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-019-00712-y","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W37385681","https://openalex.org/W564046778","https://openalex.org/W584522352","https://openalex.org/W636443671","https://openalex.org/W1486768134","https://openalex.org/W1568909586","https://openalex.org/W1595198957","https://openalex.org/W1969405923","https://openalex.org/W1976677460","https://openalex.org/W1989150101","https://openalex.org/W2004502213","https://openalex.org/W2044084198","https://openalex.org/W2046341875","https://openalex.org/W2058368307","https://openalex.org/W2063388923","https://openalex.org/W2085921935","https://openalex.org/W2090432705","https://openalex.org/W2093861211","https://openalex.org/W2100677873","https://openalex.org/W2159757394","https://openalex.org/W2161635222","https://openalex.org/W2285925216","https://openalex.org/W2309179828","https://openalex.org/W2477775364","https://openalex.org/W2504274129","https://openalex.org/W2597283313","https://openalex.org/W2808611543","https://openalex.org/W2970864062","https://openalex.org/W4205545339","https://openalex.org/W4234629858"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper":[3],"we":[4,47],"prove":[5],"that":[6,49],"in":[7,30],"opposite":[8],"to":[9],"the":[10,17,23],"cases":[11],"of":[12,26,54],"6":[13],"and":[14,63],"8":[15],"variables,":[16],"Maiorana-McFarland":[18],"construction":[19],"does":[20],"not":[21],"describe":[22],"whole":[24],"class":[25],"cubic":[27],"bent":[28],"functions":[29,58],"n":[31,55],"variables":[32],"for":[33,50],"all":[34,52],"$$n\\ge":[35],"10$$":[36],"<mml:math":[37],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[38],"<mml:mrow>":[39],"<mml:mi>n</mml:mi>":[40],"<mml:mo>\u2265</mml:mo>":[41],"<mml:mn>10</mml:mn>":[42],"</mml:mrow>":[43],"</mml:math>":[44],".":[45],"Moreover,":[46],"show":[48],"almost":[51],"values":[53],",":[56],"these":[57],"can":[59],"simultaneously":[60],"be":[61],"homogeneous":[62],"have":[64],"no":[65],"affine":[66],"derivatives.":[67]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2019-09-05T00:00:00"}