{"id":"https://openalex.org/W2102799756","doi":"https://doi.org/10.1109/tit.2014.2317698","title":"An Improvement to Levenshtein's Upper Bound on the Cardinality of Deletion Correcting Codes","display_name":"An Improvement to Levenshtein's Upper Bound on the Cardinality of Deletion Correcting Codes","publication_year":2014,"publication_date":"2014-04-16","ids":{"openalex":"https://openalex.org/W2102799756","doi":"https://doi.org/10.1109/tit.2014.2317698","mag":"2102799756"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2014.2317698","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2317698","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/A5089243170","display_name":"Daniel Cullina","orcid":"https://orcid.org/0000-0002-7471-2102"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Daniel Cullina","raw_affiliation_strings":["Department of Electrical and Computer Engineering and Coordinated Science Laboratory, University of Illinois at Champaign-Urbana, Urbana, IL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering and Coordinated Science Laboratory, University of Illinois at Champaign-Urbana, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012789968","display_name":"Negar Kiyavash","orcid":"https://orcid.org/0000-0002-8545-7709"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Negar Kiyavash","raw_affiliation_strings":["Department of Industrial and Enterprise Systems Engineering and Coordinated Science Laboratory, University of Illinois at Champaign-Urbana, Urbana, IL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and Enterprise Systems Engineering and Coordinated Science Laboratory, University of Illinois at Champaign-Urbana, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089243170"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":1.9521,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.86226018,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"60","issue":"7","first_page":"3862","last_page":"3870"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10207","display_name":"Advanced biosensing and bioanalysis techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9916999936103821,"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/combinatorics","display_name":"Combinatorics","score":0.6728823184967041},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.6717578768730164},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6645177602767944},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.6503497362136841},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5811210870742798},{"id":"https://openalex.org/keywords/levenshtein-distance","display_name":"Levenshtein distance","score":0.5669333338737488},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5029107928276062},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48222124576568604},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4373036324977875},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.4144187867641449},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2957264482975006},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26716798543930054}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6728823184967041},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6717578768730164},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6645177602767944},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.6503497362136841},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5811210870742798},{"id":"https://openalex.org/C2777515626","wikidata":"https://www.wikidata.org/wiki/Q496939","display_name":"Levenshtein distance","level":2,"score":0.5669333338737488},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5029107928276062},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48222124576568604},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4373036324977875},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.4144187867641449},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2957264482975006},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26716798543930054},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2014.2317698","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2317698","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":[],"awards":[{"id":"https://openalex.org/G6073077466","display_name":null,"funder_award_id":"FA9550-11-1-0016","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6874991541","display_name":null,"funder_award_id":"CCF 10-54937 CAR","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G69691392","display_name":null,"funder_award_id":"CCF 10-65022","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7595684426","display_name":null,"funder_award_id":"FA 9550-10-1-0573","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1502626542","https://openalex.org/W1517422340","https://openalex.org/W1647671624","https://openalex.org/W1999116222","https://openalex.org/W2074389198","https://openalex.org/W2081354249","https://openalex.org/W2091876558","https://openalex.org/W2103012681","https://openalex.org/W2115151682","https://openalex.org/W2125278308","https://openalex.org/W2127079370","https://openalex.org/W2137484241","https://openalex.org/W2170653881","https://openalex.org/W2963183421","https://openalex.org/W4233413206","https://openalex.org/W6630260739","https://openalex.org/W6636915900"],"related_works":["https://openalex.org/W2017783420","https://openalex.org/W2776473626","https://openalex.org/W4235874751","https://openalex.org/W2739495308","https://openalex.org/W2952256352","https://openalex.org/W4297612276","https://openalex.org/W2949445167","https://openalex.org/W2170653881","https://openalex.org/W2556398241","https://openalex.org/W2190053471"],"abstract_inverted_index":{"We":[0,92],"consider":[1],"deletion":[2],"correcting":[3,18],"codes":[4,60],"over":[5],"a":[6,42],"q-ary":[7],"alphabet.":[8],"It":[9],"is":[10,61,120,133],"well":[11],"known":[12,111],"that":[13,47,70],"any":[14,24],"code":[15,38],"capable":[16],"of":[17,26,51,59,65,128],"s":[19,27],"deletions":[20,129],"can":[21],"also":[22],"correct":[23],"combination":[25],"total":[28],"insertions":[29,52],"and":[30,53,86],"deletions.":[31,54],"To":[32],"obtain":[33,72],"asymptotic":[34],"upper":[35],"bounds":[36,69,80],"on":[37],"size,":[39],"we":[40,71],"apply":[41],"packing":[43],"argument":[44],"to":[45,75,82,105,130],"channels":[46],"perform":[48],"different":[49],"mixtures":[50],"Even":[55],"though":[56],"the":[57,68,79,83,87,101,109,126,136],"set":[58],"identical":[62],"for":[63,112],"all":[64],"these":[66,94],"channels,":[67],"vary.":[73],"Prior":[74],"this":[76],"paper,":[77],"only":[78],"corresponding":[81],"all-insertion":[84],"case":[85,89],"all-deletion":[88,102],"were":[90],"known.":[91],"recover":[93],"as":[95],"special":[96],"cases.":[97],"The":[98],"bound":[99,119,124],"from":[100],"case,":[103],"due":[104],"Levenshtein,":[106],"has":[107],"been":[108],"best":[110],"more":[113],"than":[114,122,135],"45":[115],"years.":[116],"Our":[117],"generalized":[118],"better":[121],"Levenshtein's":[123],"whenever":[125],"number":[127],"be":[131],"corrected":[132],"larger":[134],"alphabet":[137],"size.":[138]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}