{"id":"https://openalex.org/W4409207732","doi":"https://doi.org/10.3934/amc.2025013","title":"Counting double-polycyclic codes over a finite chain ring of nilpotency index two","display_name":"Counting double-polycyclic codes over a finite chain ring of nilpotency index two","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4409207732","doi":"https://doi.org/10.3934/amc.2025013"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2025013","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2025013","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=67f37f72fe86615edff381b3","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/data/article/export-pdf?id=67f37f72fe86615edff381b3","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001632776","display_name":"Sarra Talbi","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sarra Talbi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076246966","display_name":"Alexandre Fotue Tabue","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexandre Fotue Tabue","raw_affiliation_strings":["Department of Mathematics, Higher Teacher Training College, University of Bertoua, Cameroon"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Higher Teacher Training College, University of Bertoua, Cameroon","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053156834","display_name":"Meenakshi Devi","orcid":"https://orcid.org/0000-0001-6656-1087"},"institutions":[{"id":"https://openalex.org/I3131135081","display_name":"Sol Plaatje University","ror":"https://ror.org/01kn7bc28","country_code":"ZA","type":"education","lineage":["https://openalex.org/I3131135081"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Meenakshi Devi","raw_affiliation_strings":["Department of Mathematical Sciences, Sol Plaatje University, Private Bag X5008, Kimberley, 8300, South Africa"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Sol Plaatje University, Private Bag X5008, Kimberley, 8300, South Africa","institution_ids":["https://openalex.org/I3131135081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5001632776"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03098311,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"6","first_page":"1642","last_page":"1656"},"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":0.9918000102043152,"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":0.9912999868392944,"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/mathematics","display_name":"Mathematics","score":0.9401887655258179},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.5919390916824341},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.5826320648193359},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.5561493635177612},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.46958106756210327},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39619433879852295},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3854442536830902},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05143281817436218}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9401887655258179},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5919390916824341},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.5826320648193359},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.5561493635177612},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46958106756210327},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39619433879852295},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3854442536830902},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05143281817436218},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2025013","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2025013","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=67f37f72fe86615edff381b3","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2025013","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2025013","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=67f37f72fe86615edff381b3","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409207732.pdf","grobid_xml":"https://content.openalex.org/works/W4409207732.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W2005937113","https://openalex.org/W2063301472","https://openalex.org/W2962763807","https://openalex.org/W2963976753","https://openalex.org/W2971708712","https://openalex.org/W3118748947","https://openalex.org/W3198215848","https://openalex.org/W3214531090","https://openalex.org/W4306697274","https://openalex.org/W4392462150","https://openalex.org/W4393044532"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2980963558","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W1976691234","https://openalex.org/W3212023493","https://openalex.org/W2090715877","https://openalex.org/W2572370460"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,44],"study":[4],"the":[5,35,47,61],"algebraic":[6],"structure":[7],"of":[8,23,37,49,64],"double-polycyclic":[9,41],"codes":[10],"over":[11],"a":[12,20],"finite":[13],"chain":[14],"ring":[15],"$":[16,18,51,57,59,65],"R":[17,53,66],"with":[19],"nilpotency":[21],"index":[22],"two,":[24],"defined":[25],"by":[26],"associated":[27],"square-free":[28],"polynomials.":[29],"We":[30],"also":[31],"provide":[32],"formulas":[33],"for":[34],"number":[36,48],"separable":[38],"and":[39],"non-separable":[40,50],"codes.":[42],"Finally,":[43],"briefly":[45],"discuss":[46],"\\mathbb{F}_q":[52,58],"$-polycyclic":[54],"codes,":[55],"where":[56],"is":[60],"residue":[62],"field":[63],"$.":[67]},"counts_by_year":[],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}