{"id":"https://openalex.org/W2117430794","doi":"https://doi.org/10.1109/tit.1986.1057249","title":"Do most binary linear codes achieve the Goblick bound on the covering radius? (Corresp.)","display_name":"Do most binary linear codes achieve the Goblick bound on the covering radius? (Corresp.)","publication_year":1986,"publication_date":"1986-11-01","ids":{"openalex":"https://openalex.org/W2117430794","doi":"https://doi.org/10.1109/tit.1986.1057249","mag":"2117430794"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1986.1057249","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1986.1057249","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/A5109153224","display_name":"P. Delsarte","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. Delsarte","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5111796032","display_name":"P. Piret","orcid":null},"institutions":[{"id":"https://openalex.org/I4210159858","display_name":"Philips (Belgium)","ror":"https://ror.org/05bsjqt55","country_code":"BE","type":"company","lineage":["https://openalex.org/I4210122849","https://openalex.org/I4210159858"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"P. Piret","raw_affiliation_strings":["Philips Research National Laboratory, Brussels, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Philips Research National Laboratory, Brussels, Belgium","institution_ids":["https://openalex.org/I4210159858"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5902,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.79098162,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"32","issue":"6","first_page":"826","last_page":"828"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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":0.9990000128746033,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9902999997138977,"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/conjecture","display_name":"Conjecture","score":0.7050634622573853},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.5528822541236877},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5392642617225647},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.527367889881134},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5234771966934204},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49500077962875366},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4667178988456726},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4549138844013214},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37736454606056213},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3417094945907593},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19784247875213623},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.11392509937286377},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.08952832221984863}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7050634622573853},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5528822541236877},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5392642617225647},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.527367889881134},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5234771966934204},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49500077962875366},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4667178988456726},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4549138844013214},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37736454606056213},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3417094945907593},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19784247875213623},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.11392509937286377},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.08952832221984863},{"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1986.1057249","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1986.1057249","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/W1590624540","https://openalex.org/W1967915758","https://openalex.org/W2066791277","https://openalex.org/W2126655674","https://openalex.org/W2133397787","https://openalex.org/W2136319083","https://openalex.org/W2219576505"],"related_works":["https://openalex.org/W3194471551","https://openalex.org/W4375956809","https://openalex.org/W1581373162","https://openalex.org/W2784911598","https://openalex.org/W4297950433","https://openalex.org/W1973978937","https://openalex.org/W4287023968","https://openalex.org/W4288279572","https://openalex.org/W4286909116","https://openalex.org/W4292635168"],"abstract_inverted_index":{"The":[0,74],"following":[1],"two":[2],"problems":[3,66],"are":[4],"dealt":[5],"with:":[6],"P1)":[7],"finding":[8],"the":[9,51,56,91,99,111,116,120,146],"smallest":[10],"rate,":[11],"<tex":[12,22,30,47,79],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[13,23,31,48,80],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">R</tex>":[14,49],",":[15],"of":[16,20,40,58,103,135,145],"a":[17,26,38,62,141],"binary":[18],"code":[19],"length":[21],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</tex>":[24],"admitting":[25],"prescribed":[27],"covering":[28,53],"radius":[29],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\rho":[32],"n</tex>":[33],";":[34],"P2)":[35],"discovering":[36],"whether":[37],"majority":[39],"codes":[41,61],"with":[42],"any":[43],"rate":[44],"larger":[45],"than":[46],"admits":[50],"given":[52],"radius.":[54],"For":[55],"class":[57,102],"unrestricted":[59,121],"(nonlinear)":[60],"solution":[63,75,112],"to":[64,76,93,113,127],"both":[65],"is":[67,78,95,115,138,143],"obtained":[68],"by":[69],"an":[70,129],"elementary":[71],"averaging":[72],"argument.":[73],"P1":[77,114],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">R":[81],"=":[82],"1":[83],"-":[84],"H(\\rho)":[85],"+":[86],"O(n^{-1}":[87],"\\log":[88],"n)</tex>":[89],"and":[90,140],"answer":[92],"P2":[94,125,150],"positive.":[96],"As":[97],"for":[98,151],"more":[100],"interesting":[101],"linear":[104,152],"codes,":[105],"Goblick's":[106,136],"extension":[107],"method":[108],"shows":[109],"that":[110],"same":[117],"as":[118],"in":[119,123],"case;":[122],"contrast,":[124],"seems":[126],"remain":[128],"open":[130],"question.":[131],"A":[132],"simple":[133],"derivation":[134],"result":[137],"presented,":[139],"discussion":[142],"made":[144],"positive":[147],"conjecture":[148],"concerning":[149],"codes.":[153]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}