{"id":"https://openalex.org/W2921758813","doi":"https://doi.org/10.1007/s00200-019-00384-0","title":"On codes over Frobenius rings: generating characters, MacWilliams identities and generator matrices","display_name":"On codes over Frobenius rings: generating characters, MacWilliams identities and generator matrices","publication_year":2019,"publication_date":"2019-03-07","ids":{"openalex":"https://openalex.org/W2921758813","doi":"https://doi.org/10.1007/s00200-019-00384-0","mag":"2921758813"},"language":"en","primary_location":{"id":"doi:10.1007/s00200-019-00384-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00200-019-00384-0","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/A5059969175","display_name":"Steven T. Dougherty","orcid":"https://orcid.org/0000-0003-4877-1923"},"institutions":[{"id":"https://openalex.org/I124113063","display_name":"University of Scranton","ror":"https://ror.org/05xwb6v37","country_code":"US","type":"education","lineage":["https://openalex.org/I124113063"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Steven T. Dougherty","raw_affiliation_strings":["Department of Mathematics, University of Scranton, Scranton, PA, 18510, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Scranton, Scranton, PA, 18510, USA","institution_ids":["https://openalex.org/I124113063"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008219317","display_name":"Eseng\u00fcl Salturk","orcid":"https://orcid.org/0000-0003-1409-1102"},"institutions":[{"id":"https://openalex.org/I124113063","display_name":"University of Scranton","ror":"https://ror.org/05xwb6v37","country_code":"US","type":"education","lineage":["https://openalex.org/I124113063"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eseng\u00fcl Salt\u00fcrk","raw_affiliation_strings":["Department of Mathematics, University of Scranton, Scranton, PA, 18510, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Scranton, Scranton, PA, 18510, USA","institution_ids":["https://openalex.org/I124113063"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010031419","display_name":"Steve Szabo","orcid":"https://orcid.org/0000-0002-0523-5162"},"institutions":[{"id":"https://openalex.org/I110325482","display_name":"Eastern Kentucky University","ror":"https://ror.org/012xks909","country_code":"US","type":"education","lineage":["https://openalex.org/I110325482"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Steve Szabo","raw_affiliation_strings":["Department of Mathematics and Statistics, Eastern Kentucky University, Richmond, KY, 40475, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Eastern Kentucky University, Richmond, KY, 40475, USA","institution_ids":["https://openalex.org/I110325482"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010031419"],"corresponding_institution_ids":["https://openalex.org/I110325482"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.1445,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.55162445,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"30","issue":"3","first_page":"193","last_page":"206"},"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/T10849","display_name":"Finite Group Theory Research","score":0.9958999752998352,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9945999979972839,"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/generator-matrix","display_name":"Generator matrix","score":0.7498557567596436},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6456753611564636},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.6404623985290527},{"id":"https://openalex.org/keywords/character","display_name":"Character (mathematics)","score":0.6063946485519409},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.576937735080719},{"id":"https://openalex.org/keywords/local-ring","display_name":"Local ring","score":0.5671850442886353},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.5661272406578064},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.5486134886741638},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.49202463030815125},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.47122466564178467},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44752466678619385},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4426649808883667},{"id":"https://openalex.org/keywords/canonical-form","display_name":"Canonical form","score":0.4273379147052765},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.18583041429519653},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11454474925994873},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.0659303367137909},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.04724305868148804},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04167020320892334}],"concepts":[{"id":"https://openalex.org/C1842014","wikidata":"https://www.wikidata.org/wiki/Q1502046","display_name":"Generator matrix","level":3,"score":0.7498557567596436},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6456753611564636},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.6404623985290527},{"id":"https://openalex.org/C2780861071","wikidata":"https://www.wikidata.org/wiki/Q1062934","display_name":"Character (mathematics)","level":2,"score":0.6063946485519409},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.576937735080719},{"id":"https://openalex.org/C142109727","wikidata":"https://www.wikidata.org/wiki/Q1142704","display_name":"Local ring","level":3,"score":0.5671850442886353},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5661272406578064},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.5486134886741638},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49202463030815125},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.47122466564178467},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44752466678619385},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4426649808883667},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.4273379147052765},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.18583041429519653},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11454474925994873},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0659303367137909},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.04724305868148804},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04167020320892334},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00200-019-00384-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00200-019-00384-0","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":[{"id":"https://openalex.org/F4320312459","display_name":"University of Scranton","ror":"https://ror.org/05xwb6v37"},{"id":"https://openalex.org/F4320322626","display_name":"T\u00fcrkiye Bilimsel ve Teknolojik Ara\u015ft\u0131rma Kurumu","ror":"https://ror.org/04w9kkr77"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W151567740","https://openalex.org/W1787518919","https://openalex.org/W1973174922","https://openalex.org/W2023474657","https://openalex.org/W2031685689","https://openalex.org/W2056472639","https://openalex.org/W2162724186","https://openalex.org/W2168674495","https://openalex.org/W2190150863","https://openalex.org/W2346160770","https://openalex.org/W2406976870","https://openalex.org/W4229893300"],"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":2025,"cited_by_count":3},{"year":2024,"cited_by_count":8},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
