{"id":"https://openalex.org/W3006368394","doi":"https://doi.org/10.1007/s10623-020-00733-y","title":"Upper bounds for energies of spherical codes of given cardinality and separation","display_name":"Upper bounds for energies of spherical codes of given cardinality and separation","publication_year":2020,"publication_date":"2020-02-15","ids":{"openalex":"https://openalex.org/W3006368394","doi":"https://doi.org/10.1007/s10623-020-00733-y","mag":"3006368394"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-020-00733-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-020-00733-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":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/A5026823761","display_name":"Peter Boyvalenkov","orcid":"https://orcid.org/0000-0001-7563-9552"},"institutions":[{"id":"https://openalex.org/I178498160","display_name":"American University in Bulgaria","ror":"https://ror.org/05n8fe870","country_code":"BG","type":"education","lineage":["https://openalex.org/I178498160"]},{"id":"https://openalex.org/I24768866","display_name":"Bulgarian Academy of Sciences","ror":"https://ror.org/01x8hew03","country_code":"BG","type":"government","lineage":["https://openalex.org/I24768866"]},{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]}],"countries":["BG"],"is_corresponding":true,"raw_author_name":"P. G. Boyvalenkov","raw_affiliation_strings":["Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 G Bonchev Str., 1113, Sofia, Bulgaria","Technical Faculty, South-Western University, Blagoevgrad, Bulgaria"],"raw_orcid":"https://orcid.org/0000-0001-7563-9552","affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 G Bonchev Str., 1113, Sofia, Bulgaria","institution_ids":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]},{"raw_affiliation_string":"Technical Faculty, South-Western University, Blagoevgrad, Bulgaria","institution_ids":["https://openalex.org/I178498160"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054394123","display_name":"Peter D Dragnev","orcid":"https://orcid.org/0000-0001-7039-3047"},"institutions":[{"id":"https://openalex.org/I4210130184","display_name":"Purdue University Fort Wayne","ror":"https://ror.org/04c4hz115","country_code":"US","type":"education","lineage":["https://openalex.org/I4210130184"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. D. Dragnev","raw_affiliation_strings":["Department of Mathematical Sciences, Purdue University Fort Wayne, Fort Wayne, IN, 46805, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Purdue University Fort Wayne, Fort Wayne, IN, 46805, USA","institution_ids":["https://openalex.org/I4210130184"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066655505","display_name":"Douglas P. Hardin","orcid":"https://orcid.org/0000-0003-0867-2146"},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. P. Hardin","raw_affiliation_strings":["Department of Mathematics, Center for Constructive Approximation, Vanderbilt University, Nashville, TN, 37240, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Center for Constructive Approximation, Vanderbilt University, Nashville, TN, 37240, USA","institution_ids":["https://openalex.org/I200719446"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045775858","display_name":"Edward B. Saff","orcid":"https://orcid.org/0000-0003-1079-9074"},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E. B. Saff","raw_affiliation_strings":["Department of Mathematics, Center for Constructive Approximation, Vanderbilt University, Nashville, TN, 37240, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Center for Constructive Approximation, Vanderbilt University, Nashville, TN, 37240, USA","institution_ids":["https://openalex.org/I200719446"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049146864","display_name":"Maya Stoyanova","orcid":"https://orcid.org/0000-0002-8813-3398"},"institutions":[{"id":"https://openalex.org/I58918642","display_name":"Sofia University \"St. Kliment Ohridski\"","ror":"https://ror.org/02jv3k292","country_code":"BG","type":"education","lineage":["https://openalex.org/I58918642"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"M. M. Stoyanova","raw_affiliation_strings":["Faculty of Mathematics and Informatics, Sofia University, 5 James Bourchier Blvd., 1164, Sofia, Bulgaria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Informatics, Sofia University, 5 James Bourchier Blvd., 1164, Sofia, Bulgaria","institution_ids":["https://openalex.org/I58918642"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5026823761"],"corresponding_institution_ids":["https://openalex.org/I178498160","https://openalex.org/I24768866","https://openalex.org/I4210105926"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.5473,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.58178487,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"88","issue":"9","first_page":"1811","last_page":"1826"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9843999743461609,"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/T11476","display_name":"Graph theory and applications","score":0.9584000110626221,"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/cardinality","display_name":"Cardinality (data modeling)","score":0.7601523399353027},{"id":"https://openalex.org/keywords/separation","display_name":"Separation (statistics)","score":0.684638261795044},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4262031316757202},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3710242509841919},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2759544253349304},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17849239706993103},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.07294780015945435}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.7601523399353027},{"id":"https://openalex.org/C2776061190","wikidata":"https://www.wikidata.org/wiki/Q7451805","display_name":"Separation (statistics)","level":2,"score":0.684638261795044},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4262031316757202},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3710242509841919},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2759544253349304},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17849239706993103},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.07294780015945435}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10623-020-00733-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-020-00733-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":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":[{"id":"https://metadata.un.org/sdg/7","score":0.7699999809265137,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G1327117976","display_name":null,"funder_award_id":"DO1-205/23.11.2018","funder_id":"https://openalex.org/F4320321842","funder_display_name":"Ministry of Education, Youth and Science"},{"id":"https://openalex.org/G3968759571","display_name":null,"funder_award_id":"DMS-1516400","funder_id":"https://openalex.org/F4320332172","funder_display_name":"Directorate for Mathematical and Physical Sciences"},{"id":"https://openalex.org/G6214083909","display_name":null,"funder_award_id":"282207","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"}],"funders":[{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320321842","display_name":"Ministry of Education, Youth and Science","ror":"https://ror.org/053pcb396"},{"id":"https://openalex.org/F4320332172","display_name":"Directorate for Mathematical and Physical Sciences","ror":"https://ror.org/029b7h395"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1556443961","https://openalex.org/W1559601530","https://openalex.org/W1814198588","https://openalex.org/W1879145692","https://openalex.org/W1963785789","https://openalex.org/W1974310186","https://openalex.org/W1986015715","https://openalex.org/W1992895663","https://openalex.org/W2013083117","https://openalex.org/W2018627370","https://openalex.org/W2028783114","https://openalex.org/W2035407233","https://openalex.org/W2045685925","https://openalex.org/W2054085030","https://openalex.org/W2073476719","https://openalex.org/W2089861794","https://openalex.org/W2101504517","https://openalex.org/W2142823474","https://openalex.org/W2152345982","https://openalex.org/W2234399181","https://openalex.org/W2306519013","https://openalex.org/W2584020404","https://openalex.org/W2593714566","https://openalex.org/W2795347491","https://openalex.org/W2948665967","https://openalex.org/W2951179629","https://openalex.org/W2963201988","https://openalex.org/W2963337767","https://openalex.org/W2963419410","https://openalex.org/W2964035426","https://openalex.org/W2964071657","https://openalex.org/W2964204556","https://openalex.org/W2981112152","https://openalex.org/W2988614387","https://openalex.org/W3021418914","https://openalex.org/W3038165843","https://openalex.org/W3097981526","https://openalex.org/W3103274847","https://openalex.org/W3103309976","https://openalex.org/W4231202173","https://openalex.org/W4240172225","https://openalex.org/W4254849512","https://openalex.org/W4295022726","https://openalex.org/W6666140858"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2002177687","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}