{"id":"https://openalex.org/W2325795067","doi":"https://doi.org/10.1142/s1793830916500361","title":"On the linear codes over the ring Rp","display_name":"On the linear codes over the ring Rp","publication_year":2016,"publication_date":"2016-03-30","ids":{"openalex":"https://openalex.org/W2325795067","doi":"https://doi.org/10.1142/s1793830916500361","mag":"2325795067"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830916500361","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830916500361","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","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/A5071226571","display_name":"Abdullah Dertli","orcid":"https://orcid.org/0000-0001-8687-032X"},"institutions":[{"id":"https://openalex.org/I227306068","display_name":"Ondokuz May\u0131s University","ror":"https://ror.org/028k5qw24","country_code":"TR","type":"education","lineage":["https://openalex.org/I227306068"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Abdullah Dertli","raw_affiliation_strings":["Mathematics Department, Faculty of Arts and Sciences, Ondokuz May\u0131s University, Samsun, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Arts and Sciences, Ondokuz May\u0131s University, Samsun, Turkey","institution_ids":["https://openalex.org/I227306068"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058030392","display_name":"Yasemin \u00c7engellenmi\u015f","orcid":"https://orcid.org/0000-0002-8133-9836"},"institutions":[{"id":"https://openalex.org/I12387023","display_name":"Trakya University","ror":"https://ror.org/00xa0xn82","country_code":"TR","type":"education","lineage":["https://openalex.org/I12387023"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Yasemin Cengellenmis","raw_affiliation_strings":["Mathematics Department, Faculty of Arts and Sciences, Trakya University, Edirne, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Arts and Sciences, Trakya University, Edirne, Turkey","institution_ids":["https://openalex.org/I12387023"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044039598","display_name":"\u015eenol Eren","orcid":"https://orcid.org/0000-0002-8277-8056"},"institutions":[{"id":"https://openalex.org/I227306068","display_name":"Ondokuz May\u0131s University","ror":"https://ror.org/028k5qw24","country_code":"TR","type":"education","lineage":["https://openalex.org/I227306068"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Senol Eren","raw_affiliation_strings":["Mathematics Department, Faculty of Arts and Sciences, Ondokuz May\u0131s University, Samsun, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Arts and Sciences, Ondokuz May\u0131s University, Samsun, Turkey","institution_ids":["https://openalex.org/I227306068"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4416,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.77986808,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"08","issue":"02","first_page":"1650036","last_page":"1650036"},"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9993000030517578,"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/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/skew","display_name":"Skew","score":0.8798339366912842},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.693261444568634},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.5551326274871826},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.513782799243927},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.475458562374115},{"id":"https://openalex.org/keywords/cyclic-code","display_name":"Cyclic code","score":0.47206050157546997},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.43029487133026123},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4139164388179779},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.38073107600212097},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2263249158859253},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.20917892456054688},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10959053039550781},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.06524094939231873}],"concepts":[{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.8798339366912842},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.693261444568634},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5551326274871826},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.513782799243927},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.475458562374115},{"id":"https://openalex.org/C2096984","wikidata":"https://www.wikidata.org/wiki/Q245464","display_name":"Cyclic code","level":5,"score":0.47206050157546997},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.43029487133026123},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4139164388179779},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.38073107600212097},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2263249158859253},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.20917892456054688},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10959053039550781},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.06524094939231873},{"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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830916500361","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830916500361","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W171226018","https://openalex.org/W171452924","https://openalex.org/W1975802161","https://openalex.org/W1976721628","https://openalex.org/W1999706070","https://openalex.org/W2022092822","https://openalex.org/W2031448371","https://openalex.org/W2038681062","https://openalex.org/W2055847390","https://openalex.org/W2063592138","https://openalex.org/W2070707892","https://openalex.org/W2076107177","https://openalex.org/W2097917078","https://openalex.org/W2105512769","https://openalex.org/W2105694437","https://openalex.org/W2108964585","https://openalex.org/W2131418871","https://openalex.org/W2148105168","https://openalex.org/W2151359594","https://openalex.org/W2160996071","https://openalex.org/W2165735902","https://openalex.org/W2167413626","https://openalex.org/W2167630796","https://openalex.org/W2167697875","https://openalex.org/W2169469099","https://openalex.org/W2199077741","https://openalex.org/W2320727005","https://openalex.org/W2409058913","https://openalex.org/W2505046677","https://openalex.org/W2523136389"],"related_works":["https://openalex.org/W2553897681","https://openalex.org/W3005564926","https://openalex.org/W2416281007","https://openalex.org/W1840751364","https://openalex.org/W2767158615","https://openalex.org/W2380560957","https://openalex.org/W2612958071","https://openalex.org/W4312970405","https://openalex.org/W2765886778","https://openalex.org/W3097959888"],"abstract_inverted_index":{"Some":[0],"results":[1],"are":[2,40,49,87,112,124,135],"generalized":[3],"on":[4,64],"linear":[5,129],"codes":[6,35,48,53,82,95,107,119,130],"over":[7,36,54,83,96,108,120,131],"[Formula:":[8,16,20,37,55,61,67,84,97,109,121,132],"see":[9,17,21,38,56,62,68,85,98,110,122,133],"text]":[10,22,39,63,69,86,99,111,123,134],"in":[11],"[15]":[12],"to":[13],"the":[14,65,75],"ring":[15,66],"text],":[18],"where":[19],"is":[23,70,100],"an":[24],"odd":[25],"prime":[26],"number.":[27],"The":[28,42,89,102,114],"Gray":[29,103],"images":[30,104],"of":[31,44,91,105,128],"cyclic":[32,94],"and":[33,116],"quasi-cyclic":[34],"obtained.":[41,113],"parameters":[43],"quantum":[45],"error":[46],"correcting":[47],"obtained":[50],"from":[51],"negacyclic":[52],"text].":[57],"A":[58],"nontrivial":[59],"automorphism":[60],"determined.":[71],"By":[72],"using":[73],"this,":[74],"skew":[76,78,80,93,106,117],"cyclic,":[77],"quasi-cyclic,":[79],"constacyclic":[81],"introduced.":[88,125],"number":[90],"distinct":[92],"given.":[101,136],"quasi-constacyclic":[115,118],"MacWilliams":[126],"identities":[127]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
