{"id":"https://openalex.org/W2087945452","doi":"https://doi.org/10.1109/tit.2013.2266398","title":"Quasi-Perfect Codes From Cayley Graphs Over Integer Rings","display_name":"Quasi-Perfect Codes From Cayley Graphs Over Integer Rings","publication_year":2013,"publication_date":"2013-06-06","ids":{"openalex":"https://openalex.org/W2087945452","doi":"https://doi.org/10.1109/tit.2013.2266398","mag":"2087945452"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2013.2266398","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2266398","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/A5041191073","display_name":"C\u00e1tia Quilles Queiroz","orcid":null},"institutions":[{"id":"https://openalex.org/I23925101","display_name":"Universidade Federal de Alfenas","ror":"https://ror.org/034vpja60","country_code":"BR","type":"education","lineage":["https://openalex.org/I23925101"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Catia Quilles Queiroz","raw_affiliation_strings":["Department of Mathematics, Universidade Federal de Alfenas, Alfenas, Minas Gerais, Brazil","Dept. of Math., Univ. Fed. de Alfenas, Alfenas, Brazil"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Universidade Federal de Alfenas, Alfenas, Minas Gerais, Brazil","institution_ids":["https://openalex.org/I23925101"]},{"raw_affiliation_string":"Dept. of Math., Univ. Fed. de Alfenas, Alfenas, Brazil","institution_ids":["https://openalex.org/I23925101"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025233291","display_name":"Crist\u00f3bal Camarero","orcid":"https://orcid.org/0000-0001-6418-2614"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Cristobal Camarero","raw_affiliation_strings":["Department of Computers and Electronics, Universidad de Cantabria, Santander, Cantabria, Spain","Dept. of Comput. & Electron., Univ. de Cantabria, Santander, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Computers and Electronics, Universidad de Cantabria, Santander, Cantabria, Spain","institution_ids":["https://openalex.org/I13134134"]},{"raw_affiliation_string":"Dept. of Comput. & Electron., Univ. de Cantabria, Santander, Spain","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024466118","display_name":"Carmen Mart\u00ednez","orcid":"https://orcid.org/0000-0002-9815-239X"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Carmen Martinez","raw_affiliation_strings":["Department of Computers and Electronics, Universidad de Cantabria, Santander, Cantabria, Spain","Dept. of Comput. & Electron., Univ. de Cantabria, Santander, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Computers and Electronics, Universidad de Cantabria, Santander, Cantabria, Spain","institution_ids":["https://openalex.org/I13134134"]},{"raw_affiliation_string":"Dept. of Comput. & Electron., Univ. de Cantabria, Santander, Spain","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021089630","display_name":"Reginaldo Palazzo","orcid":"https://orcid.org/0000-0002-3219-8061"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Reginaldo Palazzo","raw_affiliation_strings":["Department of Telematics, Universidade Estadual de Campinas, Campinas, Sao Paulo, Brazil","Dept. of Telematics, Univ. Estadual de Campinas, Campinas, Brazil"],"affiliations":[{"raw_affiliation_string":"Department of Telematics, Universidade Estadual de Campinas, Campinas, Sao Paulo, Brazil","institution_ids":["https://openalex.org/I181391015"]},{"raw_affiliation_string":"Dept. of Telematics, Univ. Estadual de Campinas, Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5041191073"],"corresponding_institution_ids":["https://openalex.org/I23925101"],"apc_list":null,"apc_paid":null,"fwci":0.9618,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.82560204,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"59","issue":"9","first_page":"5905","last_page":"5916"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9987999796867371,"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/mathematics","display_name":"Mathematics","score":0.6965268850326538},{"id":"https://openalex.org/keywords/perfect-power","display_name":"Perfect power","score":0.602823793888092},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.5522491931915283},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5497496724128723},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5073849558830261},{"id":"https://openalex.org/keywords/luby-transform-code","display_name":"Luby transform code","score":0.4770626127719879},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.45215532183647156},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.4435253441333771},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.4231283664703369},{"id":"https://openalex.org/keywords/hamming-bound","display_name":"Hamming bound","score":0.42095500230789185},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.3411881923675537},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32094040513038635},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25679469108581543},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1960681974887848}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6965268850326538},{"id":"https://openalex.org/C93446932","wikidata":"https://www.wikidata.org/wiki/Q1972803","display_name":"Perfect power","level":2,"score":0.602823793888092},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.5522491931915283},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5497496724128723},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5073849558830261},{"id":"https://openalex.org/C128151799","wikidata":"https://www.wikidata.org/wiki/Q13563306","display_name":"Luby transform code","level":5,"score":0.4770626127719879},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.45215532183647156},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.4435253441333771},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.4231283664703369},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.42095500230789185},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.3411881923675537},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32094040513038635},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25679469108581543},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1960681974887848},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2013.2266398","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2266398","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":22,"referenced_works":["https://openalex.org/W1788847681","https://openalex.org/W1975339667","https://openalex.org/W2022623539","https://openalex.org/W2039902841","https://openalex.org/W2055927696","https://openalex.org/W2060056811","https://openalex.org/W2070938277","https://openalex.org/W2077310184","https://openalex.org/W2107288243","https://openalex.org/W2117372643","https://openalex.org/W2130041015","https://openalex.org/W2137836566","https://openalex.org/W2142782366","https://openalex.org/W2145342924","https://openalex.org/W2153951241","https://openalex.org/W2158988585","https://openalex.org/W2166020206","https://openalex.org/W2170215959","https://openalex.org/W4210750653","https://openalex.org/W4214772016","https://openalex.org/W4234162184","https://openalex.org/W6809831772"],"related_works":["https://openalex.org/W1976052006","https://openalex.org/W2460434904","https://openalex.org/W2121825730","https://openalex.org/W2150212378","https://openalex.org/W2131310741","https://openalex.org/W2075924030","https://openalex.org/W2124402991","https://openalex.org/W2747534004","https://openalex.org/W1675804769","https://openalex.org/W1531988574"],"abstract_inverted_index":{"The":[0,89],"problem":[1,39],"of":[2,22,40,47,82,94,102,137,163],"searching":[3,41],"for":[4,42,60,72,142,150],"perfect":[5,32,118,138],"codes":[6,24,33,44,56,75,91,119,139,153,165],"has":[7],"attracted":[8],"great":[9,48],"attention":[10],"since":[11],"the":[12,20,38,95,100,117,129,135,143,151,161,164,167],"paper":[13,133,157],"by":[14,80],"Golomb":[15],"and":[16,62,84,160,166],"Welch,":[17],"in":[18,125,131,155],"which":[19,120],"existence":[21],"these":[23],"over":[25,76],"Lee":[26,55,64,168],"metric":[27,65,77,169],"spaces":[28,78],"was":[29],"considered.":[30],"Since":[31],"are":[34,87,109,158],"not":[35],"very":[36],"common,":[37],"quasi-perfect":[43,54,74,152],"is":[45,171],"also":[46,53],"interest.":[49],"In":[50,67],"this":[51,68,132,156],"aspect,":[52],"have":[57],"been":[58],"considered":[59],"2-D":[61],"3-D":[63],"spaces.":[66],"paper,":[69],"constructive":[70],"methods":[71],"obtaining":[73],"modeled":[79],"means":[81],"Gaussian":[83],"Eisenstein-Jacobi":[85],"integers":[86],"given.":[88],"obtained":[90,154],"form":[92],"ideals":[93],"integer":[96,145],"ring":[97],"thus":[98],"preserving":[99],"property":[101],"being":[103],"geometrically":[104],"uniform":[105],"codes.":[106],"Moreover,":[107],"they":[108],"able":[110],"to":[111],"correct":[112],"more":[113],"error":[114],"patterns":[115],"than":[116],"may":[121],"properly":[122],"be":[123],"used":[124],"asymmetric":[126],"channels.":[127],"Therefore,":[128],"results":[130],"complement":[134],"constructions":[136],"previously":[140],"done":[141],"same":[144],"rings.":[146],"Finally,":[147],"decoding":[148],"algorithms":[149],"provided":[159],"relationship":[162],"ones":[170],"investigated.":[172]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
