{"id":"https://openalex.org/W2014117013","doi":"https://doi.org/10.1109/tit.1968.1054146","title":"A weight distribution bound for linear codes","display_name":"A weight distribution bound for linear codes","publication_year":1968,"publication_date":"1968-05-01","ids":{"openalex":"https://openalex.org/W2014117013","doi":"https://doi.org/10.1109/tit.1968.1054146","mag":"2014117013"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1968.1054146","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1968.1054146","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/A5034773475","display_name":"Jean-Jacques L\u00e9vy","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J. Levy","raw_affiliation_strings":["ADCOM, Inc., Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"ADCOM, Inc., Cambridge, MA, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034773475"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6924,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.87073109,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"14","issue":"3","first_page":"487","last_page":"490"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9958999752998352,"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"}},{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.989300012588501,"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/code","display_name":"Code (set theory)","score":0.6251909732818604},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4463287889957428},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43847617506980896},{"id":"https://openalex.org/keywords/weight-distribution","display_name":"Weight distribution","score":0.43406394124031067},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4268539547920227},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4121500253677368},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4078773260116577},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3937567174434662},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3504226803779602},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12761926651000977},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.12213870882987976},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08629098534584045}],"concepts":[{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.6251909732818604},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4463287889957428},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43847617506980896},{"id":"https://openalex.org/C25432639","wikidata":"https://www.wikidata.org/wiki/Q3711790","display_name":"Weight distribution","level":2,"score":0.43406394124031067},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4268539547920227},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4121500253677368},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4078773260116577},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3937567174434662},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3504226803779602},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12761926651000977},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.12213870882987976},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08629098534584045},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1968.1054146","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1968.1054146","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1972817581","https://openalex.org/W2024943671","https://openalex.org/W2040009340","https://openalex.org/W2048731540","https://openalex.org/W2099861043","https://openalex.org/W2153623795","https://openalex.org/W2170045753"],"related_works":["https://openalex.org/W2980963558","https://openalex.org/W2591781490","https://openalex.org/W4289238878","https://openalex.org/W2533621910","https://openalex.org/W2007625134","https://openalex.org/W2253987509","https://openalex.org/W2377508920","https://openalex.org/W4245351974","https://openalex.org/W2579163092","https://openalex.org/W2602086057"],"abstract_inverted_index":{"A":[0],"linear":[1,78,112],"code":[2,13,21,36,57],"of":[3,15,23,34,42,56,62,77,94],"block":[4],"length":[5],"n":[6],"possessing":[7],"minimum":[8],"weight":[9,16,24,32,61,69],"d":[10,47],"has":[11,107],"one":[12],"word":[14],"zero,":[17],"and":[18,100],"no":[19],"other":[20],"words":[22,58],"less":[25],"than":[26],"<tex":[27,44,64,88,95,101],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[28,45,65,89,96,102],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">d</tex>":[29],".":[30,67,104],"The":[31,105],"distribution":[33],"the":[35,40,54],"is":[37],"given":[38],"by":[39],"set":[41],"all":[43,111],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">W(j),":[46],"\\leq":[48,50],"j":[49],"n</tex>":[51],",":[52,99],"describing":[53],"number":[55],"having":[59],"a":[60,75,92],"exactly":[63],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">j</tex>":[66,103],"Exact":[68],"distributions":[70],"are":[71],"known":[72],"for":[73],"only":[74],"handful":[76],"codes.":[79,113],"This":[80],"paper":[81],"presents":[82],"an":[83],"explicit":[84],"upper":[85],"bound":[86,106],"upon":[87],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">W(j)</tex>":[90],"as":[91],"function":[93],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n,":[97],"d</tex>":[98],"general":[108],"applicability":[109],"to":[110]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
