{"id":"https://openalex.org/W1600003812","doi":"https://doi.org/10.37236/1962","title":"Perfect Codes in Cartesian Products of 2-Paths and Infinite Paths","display_name":"Perfect Codes in Cartesian Products of 2-Paths and Infinite Paths","publication_year":2005,"publication_date":"2005-11-29","ids":{"openalex":"https://openalex.org/W1600003812","doi":"https://doi.org/10.37236/1962","mag":"1600003812"},"language":"en","primary_location":{"id":"doi:10.37236/1962","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1962","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r65/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r65/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038490437","display_name":"Paul Dorbec","orcid":"https://orcid.org/0009-0007-1179-6082"},"institutions":[{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Paul Dorbec","raw_affiliation_strings":["ENS Lyon,"],"affiliations":[{"raw_affiliation_string":"ENS Lyon,","institution_ids":["https://openalex.org/I113428412"]}]},{"author_position":"last","author":{"id":null,"display_name":"Michel Mollard","orcid":null},"institutions":[{"id":"https://openalex.org/I4210155240","display_name":"Canadian Nautical Research Society","ror":"https://ror.org/04zzdbj59","country_code":"CA","type":"other","lineage":["https://openalex.org/I4210155240"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Michel Mollard","raw_affiliation_strings":["CNRS,"],"affiliations":[{"raw_affiliation_string":"CNRS,","institution_ids":["https://openalex.org/I4210155240"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038490437"],"corresponding_institution_ids":["https://openalex.org/I113428412"],"apc_list":null,"apc_paid":null,"fwci":0.7257,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.72165784,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"12","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.916100025177002,"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":0.916100025177002,"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":0.05000000074505806,"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/T10849","display_name":"Finite Group Theory Research","score":0.007699999958276749,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.816759467124939},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7420793771743774},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.7253158688545227},{"id":"https://openalex.org/keywords/hamming-bound","display_name":"Hamming bound","score":0.5847383141517639},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5282434821128845},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.509072482585907},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5038411021232605},{"id":"https://openalex.org/keywords/perfect-power","display_name":"Perfect power","score":0.4998188018798828},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4216441512107849},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.34843575954437256},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.27277663350105286},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2012125849723816},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.17398500442504883},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.09225767850875854}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.816759467124939},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7420793771743774},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.7253158688545227},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.5847383141517639},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5282434821128845},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.509072482585907},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5038411021232605},{"id":"https://openalex.org/C93446932","wikidata":"https://www.wikidata.org/wiki/Q1972803","display_name":"Perfect power","level":2,"score":0.4998188018798828},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4216441512107849},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.34843575954437256},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.27277663350105286},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2012125849723816},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.17398500442504883},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.09225767850875854},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1962","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1962","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r65/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00412652v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00412652","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The Electronic Journal of Combinatorics, 2006, 12, pp.#65","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.37236/1962","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1962","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r65/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1600003812.pdf","grobid_xml":"https://content.openalex.org/works/W1600003812.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1980073965","https://openalex.org/W2010608390","https://openalex.org/W2070938277","https://openalex.org/W3119473442","https://openalex.org/W6645048466","https://openalex.org/W6652859106","https://openalex.org/W6788737937"],"related_works":["https://openalex.org/W3080126524","https://openalex.org/W4281616504","https://openalex.org/W2160658340","https://openalex.org/W2092304488","https://openalex.org/W1998811014","https://openalex.org/W2065657096","https://openalex.org/W1480226004","https://openalex.org/W1661409767","https://openalex.org/W2166966427","https://openalex.org/W2051699953"],"abstract_inverted_index":{"We":[0],"introduce":[1],"and":[2,12,31,37],"study":[3],"a":[4],"common":[5],"generalization":[6],"of":[7,26,28,32],"1-error":[8],"binary":[9],"perfect":[10,13,22],"codes":[11,17,23],"single":[14],"error":[15],"correcting":[16],"in":[18],"Lee":[19],"metric,":[20],"namely":[21],"on":[24],"products":[25],"paths":[27],"length":[29],"2":[30],"infinite":[33],"length.":[34],"Both":[35],"existence":[36],"nonexistence":[38],"results":[39],"are":[40],"given.":[41]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
