{"id":"https://openalex.org/W4402311227","doi":"https://doi.org/10.3390/sym16091169","title":"Generator Matrices and Symmetrized Weight Enumerators of Linear Codes over Fpm + uFpm + vFpm + wFpm","display_name":"Generator Matrices and Symmetrized Weight Enumerators of Linear Codes over Fpm + uFpm + vFpm + wFpm","publication_year":2024,"publication_date":"2024-09-06","ids":{"openalex":"https://openalex.org/W4402311227","doi":"https://doi.org/10.3390/sym16091169"},"language":"en","primary_location":{"id":"doi:10.3390/sym16091169","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16091169","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/sym16091169","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022321883","display_name":"Alhanouf Ali Alhomaidhi","orcid":"https://orcid.org/0009-0002-2520-2699"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Alhanouf Ali Alhomaidhi","raw_affiliation_strings":["Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"],"raw_orcid":"https://orcid.org/0009-0002-2520-2699","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079457395","display_name":"Sami Alabiad","orcid":"https://orcid.org/0000-0002-6824-6985"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Sami Alabiad","raw_affiliation_strings":["Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-6824-6985","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048511358","display_name":"Nawal A. Alsarori","orcid":"https://orcid.org/0000-0002-9691-4979"},"institutions":[{"id":"https://openalex.org/I165259314","display_name":"Dr. Babasaheb Ambedkar Marathwada University","ror":"https://ror.org/033pfj584","country_code":"IN","type":"education","lineage":["https://openalex.org/I165259314"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Nawal A. Alsarori","raw_affiliation_strings":["Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, India"],"raw_orcid":"https://orcid.org/0000-0002-9691-4979","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, India","institution_ids":["https://openalex.org/I165259314"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.9164,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.79193681,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"16","issue":"9","first_page":"1169","last_page":"1169"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9710000157356262,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9595999717712402,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8005352020263672},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6266847848892212},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.5399581789970398},{"id":"https://openalex.org/keywords/generator-matrix","display_name":"Generator matrix","score":0.5288459062576294},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5122589468955994},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.506808340549469},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5026905536651611},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.43954765796661377},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42379987239837646},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10263112187385559},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.09080702066421509},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.0852668285369873},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.07436162233352661},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07426798343658447}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8005352020263672},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6266847848892212},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5399581789970398},{"id":"https://openalex.org/C1842014","wikidata":"https://www.wikidata.org/wiki/Q1502046","display_name":"Generator matrix","level":3,"score":0.5288459062576294},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5122589468955994},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.506808340549469},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5026905536651611},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.43954765796661377},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42379987239837646},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10263112187385559},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.09080702066421509},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0852668285369873},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.07436162233352661},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07426798343658447},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"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/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym16091169","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16091169","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:80ee642c16a7474980fcd62389e03e20","is_oa":false,"landing_page_url":"https://doaj.org/article/80ee642c16a7474980fcd62389e03e20","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"Symmetry, Vol 16, Iss 9, p 1169 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16091169","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16091169","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1973174922","https://openalex.org/W2025617386","https://openalex.org/W2046471908","https://openalex.org/W2056472639","https://openalex.org/W2068263566","https://openalex.org/W2085147719","https://openalex.org/W2317746472","https://openalex.org/W2346160770","https://openalex.org/W2601345000","https://openalex.org/W2921758813","https://openalex.org/W3047890688","https://openalex.org/W3136596203","https://openalex.org/W3213452712","https://openalex.org/W4229893300","https://openalex.org/W4239191450","https://openalex.org/W4308118975","https://openalex.org/W4394571507","https://openalex.org/W6735582636"],"related_works":["https://openalex.org/W2590472383","https://openalex.org/W2383873009","https://openalex.org/W2393580911","https://openalex.org/W2212184297","https://openalex.org/W3156456913","https://openalex.org/W3198007960","https://openalex.org/W4322759337","https://openalex.org/W2611330756","https://openalex.org/W2744489686","https://openalex.org/W2604978577"],"abstract_inverted_index":{"Let":[0],"u,v,":[1],"and":[2,8,24,33,72,120,135],"w":[3],"be":[4],"indeterminates":[5],"over":[6,60,81,128],"Fpm":[7,37],"let":[9],"R=Fpm+uFpm+vFpm+wFpm,":[10],"where":[11,41],"p":[12],"is":[13,18,43,52],"a":[14,19,34],"prime.":[15],"Then,":[16],"R":[17,119],"ring":[20],"of":[21,30,38,57,75,78,101,104,107,116,118],"order":[22,31,39,84],"p4m,":[23],"R\u2245Fpm[u,v,w]I":[25],"with":[26],"maximal":[27],"ideal":[28],"J=uFpm+vFpm+wFpm":[29],"p3m":[32],"residue":[35],"field":[36],"pm,":[40],"I":[42],"an":[44],"appropriate":[45],"ideal.":[46],"In":[47,64,83],"this":[48],"article,":[49],"the":[50,55,68,96,102,114,132],"goal":[51],"to":[53,85,95],"improve":[54],"understanding":[56],"linear":[58,76,125],"codes":[59,77,126],"local":[61],"non-chain":[62],"rings.":[63],"particular,":[65],"we":[66,88,111,130],"investigate":[67],"symmetrized":[69,136],"weight":[70,137],"enumerators":[71],"generator":[73,133],"matrices":[74,134],"length":[79],"N":[80],"R.":[82],"accomplish":[86],"that,":[87],"first":[89],"list":[90],"all":[91],"such":[92],"rings":[93],"up":[94],"isomorphism":[97],"for":[98,124],"different":[99],"values":[100],"index":[103],"nilpotency":[105],"l":[106],"J,":[108],"2\u2264l\u22644.":[109],"Furthermore,":[110],"fully":[112],"describe":[113],"lattice":[115],"ideals":[117],"their":[121],"orders.":[122],"Next,":[123],"C":[127],"R,":[129],"compute":[131],"enumerators,":[138],"as":[139],"shown":[140],"by":[141],"numerical":[142],"examples.":[143]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2024-09-07T00:00:00"}