{"id":"https://openalex.org/W4377091158","doi":"https://doi.org/10.1007/s10623-023-01239-z","title":"An asymptotic lower bound on the number of bent functions","display_name":"An asymptotic lower bound on the number of bent functions","publication_year":2023,"publication_date":"2023-05-19","ids":{"openalex":"https://openalex.org/W4377091158","doi":"https://doi.org/10.1007/s10623-023-01239-z"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-023-01239-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-023-01239-z","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079548577","display_name":"Vladimir N. Potapov","orcid":"https://orcid.org/0000-0001-9461-2064"},"institutions":[{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"V. N. Potapov","raw_affiliation_strings":["Sobolev Institute of Mathematics, Novosibirsk, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia","institution_ids":["https://openalex.org/I4210096862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012560464","display_name":"Anna A. Taranenko","orcid":"https://orcid.org/0000-0002-7198-8242"},"institutions":[{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"A. A. Taranenko","raw_affiliation_strings":["Sobolev Institute of Mathematics, Novosibirsk, Russia"],"raw_orcid":"https://orcid.org/0000-0002-7198-8242","affiliations":[{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia","institution_ids":["https://openalex.org/I4210096862"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005504615","display_name":"Yuriy Tarannikov","orcid":"https://orcid.org/0000-0003-2101-800X"},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]},{"id":"https://openalex.org/I4210092319","display_name":"Moscow Center For Continuous Mathematical Education","ror":"https://ror.org/00dhbnv07","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210092319"]},{"id":"https://openalex.org/I4405268144","display_name":"Moscow Center of Fundamental and Applied Mathematics","ror":"https://ror.org/000xg7d10","country_code":"RU","type":"facility","lineage":["https://openalex.org/I4405268144"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Yu. V. Tarannikov","raw_affiliation_strings":["Lomonosov Moscow State University, Moscow, Russia","Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lomonosov Moscow State University, Moscow, Russia","institution_ids":["https://openalex.org/I19880235"]},{"raw_affiliation_string":"Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia","institution_ids":["https://openalex.org/I4210092319","https://openalex.org/I4405268144"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5012560464","https://openalex.org/A5079548577"],"corresponding_institution_ids":["https://openalex.org/I4210096862"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":1.3094,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.83441515,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"92","issue":"3","first_page":"639","last_page":"651"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9987000226974487,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9884999990463257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8686342835426331},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.7873263359069824},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.7753198742866516},{"id":"https://openalex.org/keywords/bent-function","display_name":"Bent function","score":0.7385589480400085},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7057321667671204},{"id":"https://openalex.org/keywords/bent-molecular-geometry","display_name":"Bent molecular geometry","score":0.6697888970375061},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.6561743021011353},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6052988171577454},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5789299607276917},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5425806641578674},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.4687390923500061},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46059855818748474},{"id":"https://openalex.org/keywords/iterated-logarithm","display_name":"Iterated logarithm","score":0.4360659122467041},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12723562121391296}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8686342835426331},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.7873263359069824},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.7753198742866516},{"id":"https://openalex.org/C84185955","wikidata":"https://www.wikidata.org/wiki/Q4890350","display_name":"Bent function","level":3,"score":0.7385589480400085},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7057321667671204},{"id":"https://openalex.org/C138211643","wikidata":"https://www.wikidata.org/wiki/Q675211","display_name":"Bent molecular geometry","level":2,"score":0.6697888970375061},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.6561743021011353},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6052988171577454},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5789299607276917},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5425806641578674},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.4687390923500061},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46059855818748474},{"id":"https://openalex.org/C130594498","wikidata":"https://www.wikidata.org/wiki/Q2028293","display_name":"Iterated logarithm","level":3,"score":0.4360659122467041},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12723562121391296},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10623-023-01239-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-023-01239-z","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G516443015","display_name":null,"funder_award_id":"FWNF-2022-0017","funder_id":"https://openalex.org/F4320337033","funder_display_name":"Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences"}],"funders":[{"id":"https://openalex.org/F4320337033","display_name":"Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences","ror":"https://ror.org/00shc0s02"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1279378592","https://openalex.org/W1621393510","https://openalex.org/W1981357736","https://openalex.org/W1983792217","https://openalex.org/W2003667685","https://openalex.org/W2067550262","https://openalex.org/W2077153543","https://openalex.org/W2093861211","https://openalex.org/W2096255437","https://openalex.org/W2148201159","https://openalex.org/W2286164450","https://openalex.org/W2297531352","https://openalex.org/W2331749669","https://openalex.org/W2899817151","https://openalex.org/W2963844454","https://openalex.org/W3007692532","https://openalex.org/W3212703233","https://openalex.org/W4205482204","https://openalex.org/W4236140721","https://openalex.org/W4293752855"],"related_works":["https://openalex.org/W1977927882","https://openalex.org/W2750816313","https://openalex.org/W1488498670","https://openalex.org/W3028718793","https://openalex.org/W2395115528","https://openalex.org/W2808103058","https://openalex.org/W1975787693","https://openalex.org/W3028678711","https://openalex.org/W2145471026","https://openalex.org/W4220960412"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}