{"id":"https://openalex.org/W4224252718","doi":"https://doi.org/10.1007/s00200-022-00549-4","title":"\u03b4-dual codes over finite commutative semi-simple rings","display_name":"\u03b4-dual codes over finite commutative semi-simple rings","publication_year":2022,"publication_date":"2022-04-20","ids":{"openalex":"https://openalex.org/W4224252718","doi":"https://doi.org/10.1007/s00200-022-00549-4"},"language":"en","primary_location":{"id":"doi:10.1007/s00200-022-00549-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00200-022-00549-4","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","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/A5012434439","display_name":"Hai Q. Dinh","orcid":"https://orcid.org/0000-0002-6487-8803"},"institutions":[{"id":"https://openalex.org/I149910238","display_name":"Kent State University","ror":"https://ror.org/049pfb863","country_code":"US","type":"education","lineage":["https://openalex.org/I149910238"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hai Q. Dinh","raw_affiliation_strings":["Department of Mathematical Sciences, Kent State University, Warren, USA","Department of Mathematical Sciences, Kent State University, 4314, Mahoning Avenue, Warren, OH, 44483, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Kent State University, Warren, USA","institution_ids":["https://openalex.org/I149910238"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Kent State University, 4314, Mahoning Avenue, Warren, OH, 44483, USA","institution_ids":["https://openalex.org/I149910238"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076430281","display_name":"Ha T. Le","orcid":null},"institutions":[{"id":"https://openalex.org/I4210115718","display_name":"Thai Nguyen University","ror":"https://ror.org/02128gy91","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210115718"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Ha T. Le","raw_affiliation_strings":["Department of Basic Sciences, Thai Nguyen University of Economics and Business Administration, Thai Nguyen city, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, Thai Nguyen University of Economics and Business Administration, Thai Nguyen city, Vietnam","institution_ids":["https://openalex.org/I4210115718"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044769639","display_name":"Bac T. Nguyen","orcid":"https://orcid.org/0000-0001-6637-4185"},"institutions":[{"id":"https://openalex.org/I170238339","display_name":"Duy Tan University","ror":"https://ror.org/05ezss144","country_code":"VN","type":"education","lineage":["https://openalex.org/I170238339"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Bac T. Nguyen","raw_affiliation_strings":["Faculty of Natural Science, Duy Tan University, Da Nang, Vietnam","Institute of Fundamental and Applied Sciences, Duy Tan University, Ho Chi Minh City, Vietnam","Institute of Fundamental and Applied Sciences, Duy Tan University, Ho Chi Minh City, 700000, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Natural Science, Duy Tan University, Da Nang, Vietnam","institution_ids":["https://openalex.org/I170238339"]},{"raw_affiliation_string":"Institute of Fundamental and Applied Sciences, Duy Tan University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I170238339"]},{"raw_affiliation_string":"Institute of Fundamental and Applied Sciences, Duy Tan University, Ho Chi Minh City, 700000, Vietnam","institution_ids":["https://openalex.org/I170238339"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049362452","display_name":"Paravee Maneejuk","orcid":"https://orcid.org/0000-0002-3794-6161"},"institutions":[{"id":"https://openalex.org/I48076826","display_name":"Chiang Mai University","ror":"https://ror.org/05m2fqn25","country_code":"TH","type":"education","lineage":["https://openalex.org/I48076826"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Paravee Maneejuk","raw_affiliation_strings":["Centre of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand","Centre of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Chiang Mai, 52000, Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand","institution_ids":["https://openalex.org/I48076826"]},{"raw_affiliation_string":"Centre of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Chiang Mai, 52000, Thailand","institution_ids":["https://openalex.org/I48076826"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5012434439","https://openalex.org/A5044769639","https://openalex.org/A5049362452","https://openalex.org/A5076430281"],"corresponding_institution_ids":["https://openalex.org/I149910238","https://openalex.org/I170238339","https://openalex.org/I4210115718","https://openalex.org/I48076826"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.02775682,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"35","issue":"3","first_page":"315","last_page":"335"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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":0.9993000030517578,"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/T10849","display_name":"Finite Group Theory Research","score":0.9977999925613403,"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/simple","display_name":"Simple (philosophy)","score":0.6875894069671631},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.5400252342224121},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5227277874946594},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.4876014292240143},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4349871873855591},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3991504907608032},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3292786180973053},{"id":"https://openalex.org/keywords/art","display_name":"Art","score":0.09004974365234375},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.0719858705997467}],"concepts":[{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6875894069671631},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.5400252342224121},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5227277874946594},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4876014292240143},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4349871873855591},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3991504907608032},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3292786180973053},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.09004974365234375},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0719858705997467},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00200-022-00549-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00200-022-00549-4","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W162701344","https://openalex.org/W1545979482","https://openalex.org/W1555131579","https://openalex.org/W1556443961","https://openalex.org/W1966896243","https://openalex.org/W1980741888","https://openalex.org/W1982432882","https://openalex.org/W1999721813","https://openalex.org/W2018650546","https://openalex.org/W2023880247","https://openalex.org/W2026316191","https://openalex.org/W2038681062","https://openalex.org/W2039466900","https://openalex.org/W2098158374","https://openalex.org/W2101436458","https://openalex.org/W2102759336","https://openalex.org/W2108964585","https://openalex.org/W2110353549","https://openalex.org/W2131202858","https://openalex.org/W2137476296","https://openalex.org/W2151359594","https://openalex.org/W2161496548","https://openalex.org/W2255090476","https://openalex.org/W2566134148","https://openalex.org/W2586200506","https://openalex.org/W2612958071","https://openalex.org/W2891992737","https://openalex.org/W2962682082","https://openalex.org/W2963616848","https://openalex.org/W2963945674","https://openalex.org/W2974932074","https://openalex.org/W3125735205","https://openalex.org/W4206775542","https://openalex.org/W4235357411"],"related_works":["https://openalex.org/W4308298797","https://openalex.org/W4255963200","https://openalex.org/W2360590989","https://openalex.org/W4255391830","https://openalex.org/W2369074270","https://openalex.org/W2408222820","https://openalex.org/W2253391970","https://openalex.org/W2015466415","https://openalex.org/W2953844587","https://openalex.org/W1565509971"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}