{"id":"https://openalex.org/W3127606808","doi":"https://doi.org/10.1109/tit.2021.3056319","title":"Universal Bounds for Size and Energy of Codes of Given Minimum and Maximum Distances","display_name":"Universal Bounds for Size and Energy of Codes of Given Minimum and Maximum Distances","publication_year":2021,"publication_date":"2021-02-03","ids":{"openalex":"https://openalex.org/W3127606808","doi":"https://doi.org/10.1109/tit.2021.3056319","mag":"3127606808"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3056319","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3056319","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/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":false,"raw_author_name":"Peter G. Boyvalenkov","raw_affiliation_strings":["Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria"],"raw_orcid":"https://orcid.org/0000-0001-7563-9552","affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria","institution_ids":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]}]},{"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":"Peter D. Dragnev","raw_affiliation_strings":["Purdue University Fort Wayne, Fort Wayne, IN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Purdue University Fort Wayne, Fort Wayne, IN, 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":"Douglas P. Hardin","raw_affiliation_strings":["Center for Constructive Approximation, Vanderbilt University, Nashville, TN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Constructive Approximation, Vanderbilt University, Nashville, TN, 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":"Edward B. Saff","raw_affiliation_strings":["Center for Constructive Approximation, Vanderbilt University, Nashville, TN, USA"],"raw_orcid":"https://orcid.org/0000-0003-1079-9074","affiliations":[{"raw_affiliation_string":"Center for Constructive Approximation, Vanderbilt University, Nashville, TN, 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":"Maya M. Stoyanova","raw_affiliation_strings":["Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria"],"raw_orcid":"https://orcid.org/0000-0002-8813-3398","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria","institution_ids":["https://openalex.org/I58918642"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2601,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.62600826,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"67","issue":"6","first_page":"3569","last_page":"3584"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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":0.9998000264167786,"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/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/T11797","display_name":"graph theory and CDMA systems","score":0.9925000071525574,"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/mathematics","display_name":"Mathematics","score":0.7990124225616455},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.664465069770813},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"Minimum distance","score":0.5908359289169312},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.588219404220581},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.56236332654953},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5378517508506775},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.4884773790836334},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.452680766582489},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1013731062412262},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09656566381454468}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7990124225616455},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.664465069770813},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.5908359289169312},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.588219404220581},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.56236332654953},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5378517508506775},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.4884773790836334},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.452680766582489},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1013731062412262},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09656566381454468},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2021.3056319","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3056319","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8100000023841858,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G4942118900","display_name":null,"funder_award_id":"DMS-1516400","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8164823316","display_name":null,"funder_award_id":"DN02/2-2016","funder_id":"https://openalex.org/F4320321843","funder_display_name":"Bulgarian National Science Fund"},{"id":"https://openalex.org/G8218594627","display_name":null,"funder_award_id":"CGM #282207","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320321843","display_name":"Bulgarian National Science Fund","ror":"https://ror.org/05eg49r29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W50599486","https://openalex.org/W109405981","https://openalex.org/W1515260243","https://openalex.org/W1814198588","https://openalex.org/W1833686326","https://openalex.org/W1879145692","https://openalex.org/W1973483608","https://openalex.org/W1986015715","https://openalex.org/W2012850743","https://openalex.org/W2046195415","https://openalex.org/W2057010175","https://openalex.org/W2073732659","https://openalex.org/W2101520088","https://openalex.org/W2112090436","https://openalex.org/W2115422885","https://openalex.org/W2154554005","https://openalex.org/W2156571667","https://openalex.org/W2159038374","https://openalex.org/W2169207476","https://openalex.org/W2306519013","https://openalex.org/W2314359380","https://openalex.org/W2575056734","https://openalex.org/W2948665967","https://openalex.org/W2963316060","https://openalex.org/W3038165843","https://openalex.org/W3100370256","https://openalex.org/W3103274847","https://openalex.org/W3118326075","https://openalex.org/W4285719527","https://openalex.org/W4295022726","https://openalex.org/W6602058375","https://openalex.org/W6630749091"],"related_works":["https://openalex.org/W4287273005","https://openalex.org/W3135784370","https://openalex.org/W2776473626","https://openalex.org/W1966028935","https://openalex.org/W2109703172","https://openalex.org/W2055212704","https://openalex.org/W2168683897","https://openalex.org/W1969401961","https://openalex.org/W1971944323","https://openalex.org/W2048794010"],"abstract_inverted_index":{"We":[0],"employ":[1],"signed":[2],"measures":[3],"that":[4,53],"are":[5,57,78],"positive":[6],"definite":[7],"up":[8],"to":[9,12],"certain":[10],"degrees":[11],"establish":[13],"Levenshtein-type":[14,65],"upper":[15,83],"bounds":[16,31,56,77,84],"on":[17,32,85],"the":[18,33,55,62,73,86],"cardinality":[19],"of":[20,51,61,64,75,88,90],"codes":[21,41,52,89],"with":[22,42],"given":[23,43],"minimum":[24,92],"and":[25,28,46,69,93,96],"maximum":[26,44,94],"distances,":[27],"universal":[29],"lower":[30],"potential":[34],"energy":[35,87],"(for":[36],"absolutely":[37],"monotone":[38],"interactions)":[39],"for":[40,72],"distance":[45,49],"cardinality.":[47,97],"The":[48],"distributions":[50],"attain":[54],"found":[58],"in":[59],"terms":[60],"parameters":[63],"quadrature":[66],"formulas.":[67],"Necessary":[68],"sufficient":[70],"conditions":[71],"optimality":[74],"our":[76],"derived.":[79],"Further,":[80],"we":[81],"obtain":[82],"fixed":[91],"distances":[95]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}