{"id":"https://openalex.org/W2885938289","doi":"https://doi.org/10.1109/isit.2018.8437752","title":"The Error Probability of Generalized Perfect Codes","display_name":"The Error Probability of Generalized Perfect Codes","publication_year":2018,"publication_date":"2018-06-01","ids":{"openalex":"https://openalex.org/W2885938289","doi":"https://doi.org/10.1109/isit.2018.8437752","mag":"2885938289"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2018.8437752","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2018.8437752","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10016/28844","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027070160","display_name":"Gonzalo Vazquez-Vilar","orcid":"https://orcid.org/0000-0002-5793-1557"},"institutions":[{"id":"https://openalex.org/I2960094004","display_name":"Hospital General Universitario Gregorio Mara\u00f1\u00f3n","ror":"https://ror.org/0111es613","country_code":"ES","type":"healthcare","lineage":["https://openalex.org/I2960094004","https://openalex.org/I4210139293"]},{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Gonzalo Vazquez-Vilar","raw_affiliation_strings":["Gregorio Mara&#x00F1;&#x00F3;n Health Research Institute, Universidad Carlos III de Madrid","Universidad Carlos III de Madrid, Gregorio Mara\u00f1\u00f3n Health Research Institute"],"affiliations":[{"raw_affiliation_string":"Gregorio Mara&#x00F1;&#x00F3;n Health Research Institute, Universidad Carlos III de Madrid","institution_ids":["https://openalex.org/I50357001"]},{"raw_affiliation_string":"Universidad Carlos III de Madrid, Gregorio Mara\u00f1\u00f3n Health Research Institute","institution_ids":["https://openalex.org/I2960094004","https://openalex.org/I50357001"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012207024","display_name":"Albert Guilleni Fabregas","orcid":null},"institutions":[{"id":"https://openalex.org/I170486558","display_name":"Pompeu Fabra University","ror":"https://ror.org/04n0g0b29","country_code":"ES","type":"education","lineage":["https://openalex.org/I170486558"]},{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I11932220","display_name":"Instituci\u00f3 Catalana de Recerca i Estudis Avan\u00e7ats","ror":"https://ror.org/0371hy230","country_code":"ES","type":"nonprofit","lineage":["https://openalex.org/I11932220"]}],"countries":["ES","GB"],"is_corresponding":false,"raw_author_name":"Albert Guill\u00e9ni F\u00e0bregas","raw_affiliation_strings":["ICREA &#x0026; Universitat Pompeu Fabra University of Cambridge","ICREA & Universitat Pompeu Fabra University of Cambridge"],"affiliations":[{"raw_affiliation_string":"ICREA &#x0026; Universitat Pompeu Fabra University of Cambridge","institution_ids":["https://openalex.org/I170486558"]},{"raw_affiliation_string":"ICREA & Universitat Pompeu Fabra University of Cambridge","institution_ids":["https://openalex.org/I170486558","https://openalex.org/I11932220","https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103184697","display_name":"Sergio Verd\u00fa","orcid":"https://orcid.org/0000-0003-1254-9116"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sergio Verd\u00fa","raw_affiliation_strings":["Princeton University"],"affiliations":[{"raw_affiliation_string":"Princeton University","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5027070160"],"corresponding_institution_ids":["https://openalex.org/I2960094004","https://openalex.org/I50357001"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0675922,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"2491","last_page":"2495"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/converse","display_name":"Converse","score":0.8848503232002258},{"id":"https://openalex.org/keywords/probability-of-error","display_name":"Probability of error","score":0.5480702519416809},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.5048211216926575},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5030915141105652},{"id":"https://openalex.org/keywords/hamming-bound","display_name":"Hamming bound","score":0.5018420219421387},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5007257461547852},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.44905781745910645},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44547325372695923},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4338310956954956},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4326925575733185},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37571632862091064},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.30515655875205994},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.1707237958908081},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12746703624725342}],"concepts":[{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.8848503232002258},{"id":"https://openalex.org/C92224547","wikidata":"https://www.wikidata.org/wiki/Q1673216","display_name":"Probability of error","level":2,"score":0.5480702519416809},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5048211216926575},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5030915141105652},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.5018420219421387},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5007257461547852},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.44905781745910645},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44547325372695923},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4338310956954956},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4326925575733185},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37571632862091064},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.30515655875205994},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.1707237958908081},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12746703624725342},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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":3,"locations":[{"id":"doi:10.1109/isit.2018.8437752","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2018.8437752","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},{"id":"pmh:oai:dnet:earchivo____::3cd0124df86d88dd8702617786f5ee4d","is_oa":true,"landing_page_url":"http://hdl.handle.net/10016/28844","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/bookPart"},{"id":"pmh:oai:generic.eprints.org:1135850","is_oa":false,"landing_page_url":"http://publications.eng.cam.ac.uk/1135850/","pdf_url":null,"source":{"id":"https://openalex.org/S4406922847","display_name":"Cambridge University Engineering Department Publications Database","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference or Workshop Item"}],"best_oa_location":{"id":"pmh:oai:dnet:earchivo____::3cd0124df86d88dd8702617786f5ee4d","is_oa":true,"landing_page_url":"http://hdl.handle.net/10016/28844","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/bookPart"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5400000214576721}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1989008275","https://openalex.org/W2066873261","https://openalex.org/W2088208366","https://openalex.org/W2106864314","https://openalex.org/W2142901448","https://openalex.org/W2183449570","https://openalex.org/W2256209916","https://openalex.org/W2993330478","https://openalex.org/W4251448448","https://openalex.org/W6691821671"],"related_works":["https://openalex.org/W135568846","https://openalex.org/W2460434904","https://openalex.org/W1789159349","https://openalex.org/W1998688728","https://openalex.org/W2113911300","https://openalex.org/W2151857680","https://openalex.org/W4386066307","https://openalex.org/W832867880","https://openalex.org/W917159298","https://openalex.org/W1975697476"],"abstract_inverted_index":{"We":[0],"introduce":[1],"a":[2],"definition":[3,20],"of":[4,33],"perfect":[5],"and":[6,24],"quasi-perfect":[7],"codes":[8],"for":[9],"symmetric":[10],"channels":[11],"parametrized":[12],"by":[13],"an":[14],"auxiliary":[15],"output":[16],"distribution.":[17],"This":[18],"new":[19],"generalizes":[21],"previous":[22],"definitions":[23],"encompasses":[25],"maximum":[26],"distance":[27],"separable":[28],"codes.":[29],"The":[30],"error":[31],"probability":[32],"these":[34],"codes,":[35],"whenever":[36],"they":[37],"exist,":[38],"is":[39],"shown":[40],"to":[41],"attain":[42],"the":[43],"meta-converse":[44],"lower":[45],"bound.":[46]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
