{"id":"https://openalex.org/W2058144850","doi":"https://doi.org/10.1109/tit.2012.2196257","title":"Diameter Perfect Lee Codes","display_name":"Diameter Perfect Lee Codes","publication_year":2012,"publication_date":"2012-04-27","ids":{"openalex":"https://openalex.org/W2058144850","doi":"https://doi.org/10.1109/tit.2012.2196257","mag":"2058144850"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2012.2196257","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2196257","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1109.3475","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"P. Horak","orcid":null},"institutions":[{"id":"https://openalex.org/I4210150356","display_name":"University of Washington Tacoma","ror":"https://ror.org/05n8t2628","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701","https://openalex.org/I4210150356"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"P. Horak","raw_affiliation_strings":["Interdisciplinary Arts and Sciences, University of Washington, Tacoma, WA, USA"],"affiliations":[{"raw_affiliation_string":"Interdisciplinary Arts and Sciences, University of Washington, Tacoma, WA, USA","institution_ids":["https://openalex.org/I4210150356"]}]},{"author_position":"last","author":{"id":null,"display_name":"B. F. AlBdaiwi","orcid":null},"institutions":[{"id":"https://openalex.org/I36721946","display_name":"Kuwait University","ror":"https://ror.org/021e5j056","country_code":"KW","type":"education","lineage":["https://openalex.org/I36721946"]}],"countries":["KW"],"is_corresponding":false,"raw_author_name":"B. F. AlBdaiwi","raw_affiliation_strings":["Computer Science Department, Kuwait University, Safat, Kuwait"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Kuwait University, Safat, Kuwait","institution_ids":["https://openalex.org/I36721946"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210150356"],"apc_list":null,"apc_paid":null,"fwci":1.2464,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.81769037,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"58","issue":"8","first_page":"5490","last_page":"5499"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.6626999974250793,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.6626999974250793,"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/T11130","display_name":"Coding theory and cryptography","score":0.24269999563694,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.021700000390410423,"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/conjecture","display_name":"Conjecture","score":0.5685999989509583},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.5471000075340271},{"id":"https://openalex.org/keywords/perfect-power","display_name":"Perfect power","score":0.5091999769210815},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4848000109195709},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.47780001163482666},{"id":"https://openalex.org/keywords/hamming-bound","display_name":"Hamming bound","score":0.448199987411499},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.41029998660087585},{"id":"https://openalex.org/keywords/word-length","display_name":"Word length","score":0.4058000147342682}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6539000272750854},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5698999762535095},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5685999989509583},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.5471000075340271},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5102999806404114},{"id":"https://openalex.org/C93446932","wikidata":"https://www.wikidata.org/wiki/Q1972803","display_name":"Perfect power","level":2,"score":0.5091999769210815},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4848000109195709},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.47780001163482666},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.448199987411499},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.41029998660087585},{"id":"https://openalex.org/C3019641298","wikidata":"https://www.wikidata.org/wiki/Q625642","display_name":"Word length","level":2,"score":0.4058000147342682},{"id":"https://openalex.org/C3427991","wikidata":"https://www.wikidata.org/wiki/Q651426","display_name":"Group code","level":5,"score":0.3743000030517578},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.36890000104904175},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.3555999994277954},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.33869999647140503},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.32589998841285706},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.3037000000476837},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.29989999532699585},{"id":"https://openalex.org/C76132124","wikidata":"https://www.wikidata.org/wiki/Q5474786","display_name":"Fountain code","level":5,"score":0.2930999994277954},{"id":"https://openalex.org/C122451846","wikidata":"https://www.wikidata.org/wiki/Q5150824","display_name":"Combinatorial design","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C2780861071","wikidata":"https://www.wikidata.org/wiki/Q1062934","display_name":"Character (mathematics)","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C2778012447","wikidata":"https://www.wikidata.org/wiki/Q1034415","display_name":"Scope (computer science)","level":2,"score":0.2565999925136566},{"id":"https://openalex.org/C2096984","wikidata":"https://www.wikidata.org/wiki/Q245464","display_name":"Cyclic code","level":5,"score":0.25529998540878296},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25440001487731934}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2012.2196257","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2196257","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"},{"id":"pmh:oai:arXiv.org:1109.3475","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1109.3475","pdf_url":"https://arxiv.org/pdf/1109.3475","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1109.3475","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1109.3475","pdf_url":"https://arxiv.org/pdf/1109.3475","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W602155066","https://openalex.org/W1584248758","https://openalex.org/W1968886440","https://openalex.org/W1990315714","https://openalex.org/W1997293718","https://openalex.org/W1999992735","https://openalex.org/W2032605678","https://openalex.org/W2034099424","https://openalex.org/W2035372587","https://openalex.org/W2038908882","https://openalex.org/W2040989249","https://openalex.org/W2044256443","https://openalex.org/W2049802481","https://openalex.org/W2052354706","https://openalex.org/W2067495494","https://openalex.org/W2070270831","https://openalex.org/W2070938277","https://openalex.org/W2084772249","https://openalex.org/W2121567355","https://openalex.org/W2137836566","https://openalex.org/W2150237827","https://openalex.org/W2154119782","https://openalex.org/W2163962630"],"related_works":[],"abstract_inverted_index":{"Lee":[0,29,44,61,87,104,140],"codes":[1,14,88,105,141],"have":[2],"been":[3,16],"intensively":[4],"studied":[5],"for":[6,53,76,119,162],"more":[7],"than":[8],"40":[9],"years.":[10],"Interest":[11],"in":[12,97],"these":[13],"has":[15],"triggered":[17],"by":[18,142],"the":[19,23,26,37,129,178],"Golomb-Welch":[20],"conjecture":[21],"on":[22,149],"existence":[24,38],"of":[25,41,63,89,106,180],"perfect":[27,43,60,86,102,139],"error-correcting":[28,103],"codes.":[30,45],"In":[31],"this":[32,126,168,181],"paper,":[33],"we":[34,49],"deal":[35],"with":[36,101],"and":[39,73,121],"enumeration":[40],"diameter":[42,138],"As":[46],"main":[47],"results,":[48],"determine":[50],"all":[51],"q":[52],"which":[54],"there":[55,81,113],"exists":[56],"a":[57,98,115,134,150],"linear":[58],"diameter-4":[59,85],"code":[62,118],"word":[64,90,107],"length":[65,91,108],"n":[66,78,92,109],"over":[67,93,110],"Z":[68,111],"<sub":[69],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[70],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q</sub>":[71],",":[72],"prove":[74],"that":[75,125,146,167],"each":[77],"\u2265":[79],"3,":[80],"are":[82],"uncountable":[83],"many":[84],"Z.":[94],"This":[95,153],"is":[96,114,123,127,133,147],"strict":[99],"contrast":[100],"as":[112],"unique":[116],"such":[117],"n=3,":[120],"its":[122],"conjectured":[124],"always":[128],"case":[130],"when":[131],"2n+1":[132],"prime.":[135],"We":[136,165],"produce":[137],"an":[143,159],"algebraic":[144],"construction":[145,169],"based":[148],"group":[151],"homomorphism.":[152],"will":[154,170],"allow":[155],"us":[156],"to":[157,173],"design":[158],"efficient":[160],"algorithm":[161],"their":[163],"decoding.":[164],"hope":[166],"turn":[171],"out":[172],"be":[174],"useful":[175],"far":[176],"beyond":[177],"scope":[179],"paper.":[182]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}