{"id":"https://openalex.org/W4289655279","doi":"https://doi.org/10.1109/isit50566.2022.9834432","title":"New Bounds on the Size of Binary Codes with Large Minimum Distance","display_name":"New Bounds on the Size of Binary Codes with Large Minimum Distance","publication_year":2022,"publication_date":"2022-06-26","ids":{"openalex":"https://openalex.org/W4289655279","doi":"https://doi.org/10.1109/isit50566.2022.9834432"},"language":"en","primary_location":{"id":"doi:10.1109/isit50566.2022.9834432","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit50566.2022.9834432","pdf_url":null,"source":{"id":"https://openalex.org/S4363604560","display_name":"2022 IEEE International Symposium on Information Theory (ISIT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-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/A5064472444","display_name":"James Chin-Jen Pang","orcid":"https://orcid.org/0000-0002-0735-8967"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"James Chin-Jen Pang","raw_affiliation_strings":["University of Michgan,Department of Electrical Engineering and Computer Science,Ann Arbor,MI,USA,48109"],"affiliations":[{"raw_affiliation_string":"University of Michgan,Department of Electrical Engineering and Computer Science,Ann Arbor,MI,USA,48109","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056299839","display_name":"Hessam Mahdavifar","orcid":"https://orcid.org/0000-0001-9021-1992"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hessam Mahdavifar","raw_affiliation_strings":["University of Michgan,Department of Electrical Engineering and Computer Science,Ann Arbor,MI,USA,48109"],"affiliations":[{"raw_affiliation_string":"University of Michgan,Department of Electrical Engineering and Computer Science,Ann Arbor,MI,USA,48109","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080241056","display_name":"Sean Pradhan","orcid":"https://orcid.org/0000-0003-0957-9816"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. Sandeep Pradhan","raw_affiliation_strings":["University of Michgan,Department of Electrical Engineering and Computer Science,Ann Arbor,MI,USA,48109"],"affiliations":[{"raw_affiliation_string":"University of Michgan,Department of Electrical Engineering and Computer Science,Ann Arbor,MI,USA,48109","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5064472444"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":0.2079,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.40050636,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1963","last_page":"1968"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"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":0.9997000098228455,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/hamming-distance","display_name":"Hamming distance","score":0.7980481386184692},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7966557741165161},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7007176280021667},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5974021553993225},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5478092432022095},{"id":"https://openalex.org/keywords/binary-code","display_name":"Binary code","score":0.5211318135261536},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"Minimum distance","score":0.5161584615707397},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4666087031364441},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.44280192255973816},{"id":"https://openalex.org/keywords/hamming-bound","display_name":"Hamming bound","score":0.42369344830513},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4144873023033142},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40689995884895325},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.34096676111221313},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3253198266029358},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.18384692072868347},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16953784227371216},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.12566781044006348},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.09318068623542786},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09054920077323914},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06497707962989807}],"concepts":[{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.7980481386184692},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7966557741165161},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7007176280021667},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5974021553993225},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5478092432022095},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.5211318135261536},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.5161584615707397},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4666087031364441},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.44280192255973816},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.42369344830513},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4144873023033142},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40689995884895325},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.34096676111221313},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3253198266029358},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.18384692072868347},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16953784227371216},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.12566781044006348},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.09318068623542786},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09054920077323914},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06497707962989807},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit50566.2022.9834432","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit50566.2022.9834432","pdf_url":null,"source":{"id":"https://openalex.org/S4363604560","display_name":"2022 IEEE International Symposium on Information Theory (ISIT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W109405981","https://openalex.org/W1498820893","https://openalex.org/W1606480398","https://openalex.org/W1976543297","https://openalex.org/W1981078592","https://openalex.org/W2010992853","https://openalex.org/W2014944833","https://openalex.org/W2053716525","https://openalex.org/W2103749128","https://openalex.org/W2109084006","https://openalex.org/W2129496126","https://openalex.org/W2170716519","https://openalex.org/W2566392544","https://openalex.org/W3005799687","https://openalex.org/W3138355547","https://openalex.org/W3174972577","https://openalex.org/W3196317722","https://openalex.org/W3216369690","https://openalex.org/W6604469142","https://openalex.org/W6792262127"],"related_works":["https://openalex.org/W2614506317","https://openalex.org/W1964096323","https://openalex.org/W2951416090","https://openalex.org/W4302771537","https://openalex.org/W4285078748","https://openalex.org/W2039769487","https://openalex.org/W3201991221","https://openalex.org/W2109703172","https://openalex.org/W2364890299","https://openalex.org/W2731597386"],"abstract_inverted_index":{"Let":[0],"A(n,":[1,27,49],"d)":[2,28,50],"denote":[3],"the":[4,52,145,148,152,161],"maximum":[5],"number":[6],"of":[7,13,81,122,147],"code-words":[8],"in":[9,36,51,56,158],"a":[10,31,71,76,119],"binary":[11],"code":[12],"length":[14,82],"n":[15,65,83,101,133,139,159,170],"and":[16,23,45,91,135],"minimum":[17],"Hamming":[18],"distance":[19,54],"d.":[20],"Deriving":[21],"upper":[22,44,127,154],"lower":[24,46,72],"bounds":[25,47,128,155],"on":[26,48,75,129],"has":[29],"been":[30],"subject":[32],"for":[33,79,160],"extensive":[34],"research":[35],"coding":[37],"theory.":[38],"In":[39],"this":[40],"paper,":[41],"we":[42],"examine":[43],"high-minimum":[53],"regime,":[55],"particular,":[57],"when":[58],"$d":[59,164],"=":[60,84,95,165],"n/2":[61,96,166],"-":[62,97,99,131,137,167],"\\Theta":[63,168],"(\\sqrt":[64,169],")$.":[66,171],"We":[67],"will":[68],"first":[69,153],"provide":[70],"bound":[73],"based":[74],"cyclic":[77],"construction":[78],"codes":[80],"2":[85],"<sup":[86],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[87],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m</sup>":[88],"\u2212":[89,116],"1":[90,111],"show":[92],"that":[93],"$A\\left({n,d":[94],"{2^{c":[98],"1}}\\sqrt":[100],"}\\right)":[102],"\\geq":[103],"{n^c}$,":[104],"where":[105],"c":[106,113],"is":[107],"an":[108],"integer":[109],"with":[110,163],"\u2a7d":[112,114],"m/2":[115],"1.":[117],"With":[118],"Fourier-analytic":[120],"view":[121],"Delsarte\u2019s":[123],"linear":[124],"program,":[125],"novel":[126],"$A(n,n/2":[130],"\\sqrt":[132],"){\\text{":[134],"}}A(n,n/2":[136],"2\\sqrt":[138],")$":[140],"are":[141,151],"obtained,":[142],"and,":[143],"to":[144],"best":[146],"authors\u2019":[149],"knowledge,":[150],"scaling":[156],"polynomially":[157],"regime":[162]},"counts_by_year":[{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}