{"id":"https://openalex.org/W3007801189","doi":"https://doi.org/10.1109/redundancy48165.2019.9003329","title":"On Two Problems Concerning Universal Bounds for Codes","display_name":"On Two Problems Concerning Universal Bounds for Codes","publication_year":2019,"publication_date":"2019-10-01","ids":{"openalex":"https://openalex.org/W3007801189","doi":"https://doi.org/10.1109/redundancy48165.2019.9003329","mag":"3007801189"},"language":"en","primary_location":{"id":"doi:10.1109/redundancy48165.2019.9003329","is_oa":false,"landing_page_url":"https://doi.org/10.1109/redundancy48165.2019.9003329","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 XVI International Symposium \"Problems of Redundancy in Information and Control Systems\" (REDUNDANCY)","raw_type":"proceedings-article"},"type":"conference-paper","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 Boyvalenkov","raw_affiliation_strings":["Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria"],"raw_orcid":null,"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 Dragnev","raw_affiliation_strings":["Department of Mathematics, Purdue University Fort Wayne, Fort Wayne, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Purdue University Fort Wayne, Fort Wayne, 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 Hardin","raw_affiliation_strings":["Department of Mathematics, Vanderbilt University, Nashville, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vanderbilt University, Nashville, 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 Saff","raw_affiliation_strings":["Department of Mathematics, Vanderbilt University, Nashville, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vanderbilt University, Nashville, 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 Stoyanova","raw_affiliation_strings":["Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria"],"raw_orcid":null,"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":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"40","issue":null,"first_page":"58","last_page":"63"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9990000128746033,"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":0.9929999709129333,"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/alphabet","display_name":"Alphabet","score":0.7840220928192139},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7766380310058594},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.7648701667785645},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.7286723256111145},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6982896327972412},{"id":"https://openalex.org/keywords/levenshtein-distance","display_name":"Levenshtein distance","score":0.6913942098617554},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.555915117263794},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49684932827949524},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45497724413871765},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4489249885082245},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"Minimum distance","score":0.4328131079673767},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.42058542370796204},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3976256549358368},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3532310128211975},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.2174496352672577},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.06895685195922852}],"concepts":[{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.7840220928192139},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7766380310058594},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.7648701667785645},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.7286723256111145},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6982896327972412},{"id":"https://openalex.org/C2777515626","wikidata":"https://www.wikidata.org/wiki/Q496939","display_name":"Levenshtein distance","level":2,"score":0.6913942098617554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.555915117263794},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49684932827949524},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45497724413871765},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4489249885082245},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.4328131079673767},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.42058542370796204},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3976256549358368},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3532310128211975},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.2174496352672577},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.06895685195922852},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/redundancy48165.2019.9003329","is_oa":false,"landing_page_url":"https://doi.org/10.1109/redundancy48165.2019.9003329","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 XVI International Symposium \"Problems of Redundancy in Information and Control Systems\" (REDUNDANCY)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W109405981","https://openalex.org/W1814198588","https://openalex.org/W1879145692","https://openalex.org/W1986015715","https://openalex.org/W2013083117","https://openalex.org/W2114067035","https://openalex.org/W2115422885","https://openalex.org/W2557794481","https://openalex.org/W2988614387","https://openalex.org/W3038165843","https://openalex.org/W3103274847","https://openalex.org/W3127606808","https://openalex.org/W6604469142","https://openalex.org/W6769524929"],"related_works":["https://openalex.org/W1969401961","https://openalex.org/W2048794010","https://openalex.org/W1541021634","https://openalex.org/W2135232882","https://openalex.org/W4285078748","https://openalex.org/W1964096323","https://openalex.org/W2364890299","https://openalex.org/W2562336992","https://openalex.org/W2951416090","https://openalex.org/W4302771537"],"abstract_inverted_index":{"We":[0,21,50,72],"consider":[1],"two":[2],"problems":[3],"related":[4],"to":[5],"proofs":[6],"and":[7,17,39,69,83],"technologies":[8],"of":[9,32,60,75],"obtaining":[10],"linear":[11],"programming":[12],"bounds":[13,35,62],"for":[14,26,36,57,63,78],"codes":[15,38,65],"(spherical":[16],"in":[18],"Hamming":[19],"spaces).":[20],"develop":[22],"a":[23,27],"verification":[24],"technique":[25],"conjecture":[28,43],"concerning":[29],"the":[30,33,42,58],"optimality":[31],"Levenshtein":[34],"spherical":[37],"prove":[40],"that":[41,92],"holds":[44],"true":[45],"under":[46],"certain":[47],"mild":[48],"assumptions.":[49],"investigate":[51],"recent":[52],"conditions":[53,94],"which":[54],"are":[55,95],"sufficient":[56],"validity":[59],"Levenshtein-type":[61],"q-ary":[64],"with":[66],"given":[67],"minimum":[68],"maximum":[70],"distances.":[71],"provide":[73],"description":[74],"all":[76],"cases":[77],"lengths":[79],"n":[80],"\u2264":[81,87,89],"36":[82],"alphabet":[84],"sizes":[85],"2":[86],"q":[88],"4":[90],"such":[91],"our":[93],"fulfilled.":[96]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}