{"id":"https://openalex.org/W2101705636","doi":"https://doi.org/10.1109/tit.2013.2284211","title":"$G$-Equivalence in Group Algebras and Minimal Abelian Codes","display_name":"$G$-Equivalence in Group Algebras and Minimal Abelian Codes","publication_year":2013,"publication_date":"2013-10-02","ids":{"openalex":"https://openalex.org/W2101705636","doi":"https://doi.org/10.1109/tit.2013.2284211","mag":"2101705636"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2013.2284211","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2284211","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1203.5742","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022940033","display_name":"Raul Ant\u00f4nio Ferraz","orcid":null},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Raul Antonio Ferraz","raw_affiliation_strings":["Universidade de S\u00e3o Paulo, Instituto de Matem\u00e1tica e Estat\u00edstica, S\u00e3o Paulo, Brazil","Inst. de Mat. e Estatistica, Univ. de Sao Paulo, Sao Paulo, Brazil"],"affiliations":[{"raw_affiliation_string":"Universidade de S\u00e3o Paulo, Instituto de Matem\u00e1tica e Estat\u00edstica, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I17974374"]},{"raw_affiliation_string":"Inst. de Mat. e Estatistica, Univ. de Sao Paulo, Sao Paulo, Brazil","institution_ids":["https://openalex.org/I17974374"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062322061","display_name":"Marin\u00eas Guerreiro","orcid":null},"institutions":[{"id":"https://openalex.org/I146165071","display_name":"Universidade Federal de Vi\u00e7osa","ror":"https://ror.org/0409dgb37","country_code":"BR","type":"education","lineage":["https://openalex.org/I146165071"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Marines Guerreiro","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Universidade Federal de Vi\u00e7osa, Vi\u00e7osa, Brazil","Dept. de Mat., Univ. Fed. de Vicosa, Vicosa, Brazil"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Universidade Federal de Vi\u00e7osa, Vi\u00e7osa, Brazil","institution_ids":["https://openalex.org/I146165071"]},{"raw_affiliation_string":"Dept. de Mat., Univ. Fed. de Vicosa, Vicosa, Brazil","institution_ids":["https://openalex.org/I146165071"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062113735","display_name":"C\u00e9sar Polcino Milies","orcid":"https://orcid.org/0000-0002-8389-0533"},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Cesar Polcino Milies","raw_affiliation_strings":["Universidade de S\u00e3o Paulo, Instituto de Matem\u00e1tica e Estat\u00edstica, S\u00e3o Paulo, Brazil","Inst. de Mat. e Estatistica, Univ. de Sao Paulo, Sao Paulo, Brazil"],"affiliations":[{"raw_affiliation_string":"Universidade de S\u00e3o Paulo, Instituto de Matem\u00e1tica e Estat\u00edstica, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I17974374"]},{"raw_affiliation_string":"Inst. de Mat. e Estatistica, Univ. de Sao Paulo, Sao Paulo, Brazil","institution_ids":["https://openalex.org/I17974374"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5022940033"],"corresponding_institution_ids":["https://openalex.org/I17974374"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.09556673,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"60","issue":"1","first_page":"252","last_page":"260"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9986000061035156,"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":0.9986000061035156,"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":0.9966999888420105,"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"}},{"id":"https://openalex.org/T11409","display_name":"Advanced Wireless Network Optimization","score":0.946399986743927,"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/abelian-group","display_name":"Abelian group","score":0.8107742071151733},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7083605527877808},{"id":"https://openalex.org/keywords/g-module","display_name":"G-module","score":0.5657275319099426},{"id":"https://openalex.org/keywords/elementary-abelian-group","display_name":"Elementary abelian group","score":0.5136117935180664},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.49699047207832336},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.4943695068359375},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.4813728630542755},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4640952944755554},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.4554826617240906},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4359615445137024},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42467060685157776},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.41755998134613037},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3856281638145447},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15389689803123474},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.06806483864784241}],"concepts":[{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.8107742071151733},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7083605527877808},{"id":"https://openalex.org/C163572010","wikidata":"https://www.wikidata.org/wiki/Q2912125","display_name":"G-module","level":4,"score":0.5657275319099426},{"id":"https://openalex.org/C81008192","wikidata":"https://www.wikidata.org/wiki/Q1017231","display_name":"Elementary abelian group","level":3,"score":0.5136117935180664},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.49699047207832336},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.4943695068359375},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.4813728630542755},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4640952944755554},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4554826617240906},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4359615445137024},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42467060685157776},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.41755998134613037},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3856281638145447},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15389689803123474},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.06806483864784241},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2013.2284211","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2284211","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:1203.5742","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1203.5742","pdf_url":"https://arxiv.org/pdf/1203.5742","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"},{"id":"doi:10.48550/arxiv.1203.5742","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1203.5742","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"mag:2101705636","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1203.5742","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1203.5742","pdf_url":"https://arxiv.org/pdf/1203.5742","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1508421660","https://openalex.org/W1632324834","https://openalex.org/W1998592296","https://openalex.org/W2030104872","https://openalex.org/W2030762068","https://openalex.org/W2033773955","https://openalex.org/W2039466900","https://openalex.org/W2091650625","https://openalex.org/W2165295593","https://openalex.org/W2204722887","https://openalex.org/W2542760130","https://openalex.org/W4230191592","https://openalex.org/W6660458140"],"related_works":["https://openalex.org/W2140370547","https://openalex.org/W2804300501","https://openalex.org/W2211328231","https://openalex.org/W3163994106","https://openalex.org/W2981621657","https://openalex.org/W2953310271","https://openalex.org/W2016212398","https://openalex.org/W1967731251","https://openalex.org/W3106151291","https://openalex.org/W2092372573","https://openalex.org/W2106125437","https://openalex.org/W3143630423","https://openalex.org/W3104158196","https://openalex.org/W3006629101","https://openalex.org/W2587836610","https://openalex.org/W3016910962","https://openalex.org/W3125430547","https://openalex.org/W2951003832","https://openalex.org/W2941700051","https://openalex.org/W2950008813"],"abstract_inverted_index":{"Let":[0],"G":[1,25,52],"be":[2,77],"a":[3,9,67],"finite":[4],"abelian":[5,30,74],"group":[6,22],"and":[7,40,69,79],"F":[8],"field":[10],"such":[11],"that":[12],"char(F)":[13],"does":[14],"not":[15],"divide":[16],"|G|.":[17],"Denote":[18],"by":[19],"FG":[20,43,57],"the":[21,87],"algebra":[23],"of":[24,35,42,51],"over":[26],"F.":[27],"A":[28],"(semisimple)":[29],"code":[31],"is":[32],"an":[33,49],"ideal":[34],"FG.":[36],"Two":[37],"codes":[38,75],"I":[39,59],"J":[41,61],"are":[44],"G-equivalent":[45,78],"if":[46],"there":[47],"exists":[48],"automorphism":[50],"whose":[53],"linear":[54],"extension":[55],"to":[56,76,82],"maps":[58],"onto":[60],"In":[62],"this":[63],"paper":[64],"we":[65],"give":[66],"necessary":[68],"sufficient":[70],"condition":[71],"for":[72],"minimal":[73],"show":[80],"how":[81],"correct":[83],"some":[84],"results":[85],"in":[86],"literature.":[88]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
