{"id":"https://openalex.org/W2130212771","doi":"https://doi.org/10.1142/s1793830912500590","title":"CYCLIC CODES THROUGH $B[X;\\frac{a}{b}{\\mathbb Z}_{0}]$, WITH $\\frac{a}{b}\\in {\\mathbb Q}^{+}$ AND b = a+1, AND ENCODING","display_name":"CYCLIC CODES THROUGH $B[X;\\frac{a}{b}{\\mathbb Z}_{0}]$, WITH $\\frac{a}{b}\\in {\\mathbb Q}^{+}$ AND b = a+1, AND ENCODING","publication_year":2012,"publication_date":"2012-10-30","ids":{"openalex":"https://openalex.org/W2130212771","doi":"https://doi.org/10.1142/s1793830912500590","mag":"2130212771"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830912500590","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830912500590","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/A5101808848","display_name":"Tariq Shah","orcid":"https://orcid.org/0009-0000-7903-0701"},"institutions":[{"id":"https://openalex.org/I12469534","display_name":"Quaid-i-Azam University","ror":"https://ror.org/04s9hft57","country_code":"PK","type":"education","lineage":["https://openalex.org/I12469534"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"TARIQ SHAH","raw_affiliation_strings":["Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan","institution_ids":["https://openalex.org/I12469534"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084389443","display_name":"Antonio Aparecido de Andrade","orcid":"https://orcid.org/0000-0001-6452-2236"},"institutions":[{"id":"https://openalex.org/I879563668","display_name":"Universidade Estadual Paulista (Unesp)","ror":"https://ror.org/00987cb86","country_code":"BR","type":"education","lineage":["https://openalex.org/I879563668"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"ANTONIO APARECIDO DE ANDRADE","raw_affiliation_strings":["Department of Mathematics, S\u00e3o Paulo State University at S\u00e3o Jos\u00e9 do Rio Preto \u2013 SP, Brazil"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, S\u00e3o Paulo State University at S\u00e3o Jos\u00e9 do Rio Preto \u2013 SP, Brazil","institution_ids":["https://openalex.org/I879563668"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101808848"],"corresponding_institution_ids":["https://openalex.org/I12469534"],"apc_list":null,"apc_paid":null,"fwci":0.8563,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.79908064,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"04","issue":"04","first_page":"1250059","last_page":"1250059"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9678999781608582,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9466000199317932,"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/monoid","display_name":"Monoid","score":0.7905576229095459},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.6598517894744873},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5994331240653992},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5793797373771667},{"id":"https://openalex.org/keywords/bch-code","display_name":"BCH code","score":0.5750448703765869},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.5257483124732971},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5238447189331055},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.4881766438484192},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4354037642478943},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.4128343462944031},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.18996548652648926},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10094016790390015},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08267894387245178},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.0631374716758728}],"concepts":[{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.7905576229095459},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.6598517894744873},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5994331240653992},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5793797373771667},{"id":"https://openalex.org/C42276685","wikidata":"https://www.wikidata.org/wiki/Q795705","display_name":"BCH code","level":3,"score":0.5750448703765869},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.5257483124732971},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5238447189331055},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.4881766438484192},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4354037642478943},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4128343462944031},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.18996548652648926},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10094016790390015},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08267894387245178},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0631374716758728},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s1793830912500590","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830912500590","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"},{"id":"pmh:oai:acervodigital.unesp.br:11449/122877","is_oa":false,"landing_page_url":"http://hdl.handle.net/11449/122877","pdf_url":null,"source":{"id":"https://openalex.org/S4306400256","display_name":"Acervo Digital da Universidade Estadual Paulista (Universidade Estadual Paulista)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210115194","host_organization_name":"Funda\u00e7\u00e3o para o Desenvolvimento da UNESP","host_organization_lineage":["https://openalex.org/I4210115194"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"outro"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W382720801","https://openalex.org/W1691084778","https://openalex.org/W2003735355","https://openalex.org/W2012698420","https://openalex.org/W2015537087","https://openalex.org/W2017758698","https://openalex.org/W2046405103","https://openalex.org/W2081884887","https://openalex.org/W2296268604","https://openalex.org/W2573623072","https://openalex.org/W4301874181"],"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/W2741158649","https://openalex.org/W2253391970","https://openalex.org/W2953844587","https://openalex.org/W1565509971"],"abstract_inverted_index":{"Let":[0],"B[X;":[1],"S]":[2],"be":[3],"a":[4,27,31,58,70],"monoid":[5,21,52],"ring":[6,13,53],"with":[7],"any":[8,33],"fixed":[9],"finite":[10],"unitary":[11],"commutative":[12],"B":[14],"and":[15],"[Formula:":[16,54],"see":[17,55],"text]":[18],"is":[19,32],"the":[20,63],"S":[22],"such":[23],"that":[24],"b":[25],"=":[26,59],"+":[28],"1,":[29,60],"where":[30],"positive":[34],"integer.":[35],"In":[36],"this":[37,75],"paper":[38],"we":[39],"constructed":[40],"cyclic":[41],"codes,":[42,44,46,48],"BCH":[43],"alternant":[45],"Goppa":[47],"Srivastava":[49],"codes":[50],"through":[51],"text].":[56],"For":[57],"almost":[61],"all":[62],"results":[64],"contained":[65],"in":[66],"[16]":[67],"stands":[68],"as":[69],"very":[71],"particular":[72],"case":[73],"of":[74],"study.":[76]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
