{"id":"https://openalex.org/W2972076795","doi":"https://doi.org/10.3934/amc.2020025","title":"Repeated-root constacyclic codes of length $ 3\\ell^mp^s $","display_name":"Repeated-root constacyclic codes of length $ 3\\ell^mp^s $","publication_year":2019,"publication_date":"2019-09-12","ids":{"openalex":"https://openalex.org/W2972076795","doi":"https://doi.org/10.3934/amc.2020025","mag":"2972076795"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2020025","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2020025","pdf_url":null,"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":null,"license_id":null,"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://doi.org/10.3934/amc.2020025","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100350997","display_name":"Yan Liu","orcid":"https://orcid.org/0000-0001-6885-2857"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yan Liu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044196416","display_name":"Minjia Shi","orcid":"https://orcid.org/0000-0002-4990-6271"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Minjia Shi","raw_affiliation_strings":["Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematical Sciences, Anhui University, Hefei, Anhui 230601, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematical Sciences, Anhui University, Hefei, Anhui 230601, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012434439","display_name":"Hai Q. Dinh","orcid":"https://orcid.org/0000-0002-6487-8803"},"institutions":[{"id":"https://openalex.org/I141445968","display_name":"Ton Duc Thang University","ror":"https://ror.org/01drq0835","country_code":"VN","type":"education","lineage":["https://openalex.org/I141445968"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Hai Q. Dinh","raw_affiliation_strings":["Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam","Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I141445968"]},{"raw_affiliation_string":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I141445968"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058887761","display_name":"Songsak Sriboonchitta","orcid":"https://orcid.org/0000-0002-3511-5452"},"institutions":[{"id":"https://openalex.org/I48076826","display_name":"Chiang Mai University","ror":"https://ror.org/05m2fqn25","country_code":"TH","type":"education","lineage":["https://openalex.org/I48076826"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Songsak Sriboonchitta","raw_affiliation_strings":["Centre of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Chiang Mai 52000, Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Chiang Mai 52000, Thailand","institution_ids":["https://openalex.org/I48076826"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044196416"],"corresponding_institution_ids":["https://openalex.org/I143868143"],"apc_list":null,"apc_paid":null,"fwci":1.7435,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.88261426,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"14","issue":"2","first_page":"359","last_page":"378"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9476000070571899,"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/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.9362000226974487,"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/mathematics","display_name":"Mathematics","score":0.8230689764022827},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5435010194778442},{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.5366842746734619},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.5260905027389526},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.5236009359359741},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.438879132270813},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3747752904891968},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3443693518638611},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.19830772280693054},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1727094054222107},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07899665832519531}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8230689764022827},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5435010194778442},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.5366842746734619},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.5260905027389526},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.5236009359359741},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.438879132270813},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3747752904891968},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3443693518638611},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.19830772280693054},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1727094054222107},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07899665832519531},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2020025","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2020025","pdf_url":null,"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":null,"license_id":null,"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.2020025","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2020025","pdf_url":null,"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":null,"license_id":null,"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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1559343931","https://openalex.org/W1973673225","https://openalex.org/W1983483270","https://openalex.org/W1985655855","https://openalex.org/W2001718971","https://openalex.org/W2014597889","https://openalex.org/W2026316191","https://openalex.org/W2040936770","https://openalex.org/W2052503266","https://openalex.org/W2082432022","https://openalex.org/W2102759336","https://openalex.org/W2110353549","https://openalex.org/W2161496548","https://openalex.org/W2200841142","https://openalex.org/W2228651896","https://openalex.org/W2491329261","https://openalex.org/W2572231742","https://openalex.org/W3141217652","https://openalex.org/W3147043509","https://openalex.org/W4206775542","https://openalex.org/W4249608945"],"related_works":["https://openalex.org/W108845024","https://openalex.org/W4300125793","https://openalex.org/W2578985712","https://openalex.org/W2406961474","https://openalex.org/W2143566611","https://openalex.org/W2013740965","https://openalex.org/W588267724","https://openalex.org/W4297743441","https://openalex.org/W2952598754","https://openalex.org/W2026779193"],"abstract_inverted_index":{"<p":[0],"style='text-indent:20px;'>Let":[1],"<inline-formula><tex-math":[2,13,25,43,48,55,63,77,96,120,125],"id=\"M3\">\\begin{document}$":[3],"p":[4,27,65],"$\\end{document}</tex-math></inline-formula>":[5,16,46,51,58,123,128],"be":[6,17],"a":[7,60],"prime":[8,20],"different":[9,21],"from":[10,22],"3,":[11],"and":[12,24,38,109],"id=\"M4\">\\begin{document}$":[14],"\\ell":[15],"an":[18,105],"odd":[19],"3":[23],"id=\"M5\">\\begin{document}$":[26],"$\\end{document}</tex-math></inline-formula>.":[28,66,101],"In":[29,102],"terms":[30],"of":[31,35,41,62,71,75,85,95,111,118],"generator":[32],"polynomials,":[33],"structures":[34],"constacyclic":[36],"codes":[37,74,117],"their":[39],"duals":[40],"length":[42,76,119],"id=\"M6\">\\begin{document}$":[44],"3\\ell^mp^s":[45],"over":[47,124],"id=\"M7\">\\begin{document}$":[49],"\\mathbb{F}_q":[50,127],"are":[52,129],"established,":[53],"where":[54],"id=\"M8\">\\begin{document}$":[56],"q":[57],"is":[59,91],"power":[61],"id=\"M9\">\\begin{document}$":[64],"We":[67],"discuss":[68],"the":[69,83,92,107],"enumeration":[70,110],"all":[72,112],"cyclic":[73,116],"id=\"M10\">\\begin{document}$":[78],"3\\cdot2^s\\ell^m":[79],"$\\end{document}</tex-math></inline-formula>,":[80],"that":[81],"generalizes":[82],"construction":[84],"[<xref":[86],"ref-type=\"bibr\"":[87],"rid=\"b15\">15</xref>]":[88],"(2016),":[89],"which":[90],"special":[93],"case":[94],"id=\"M11\">\\begin{document}$":[97],"m":[98],"=":[99],"1":[100],"addition,":[103],"as":[104],"application,":[106],"characterization":[108],"linear":[113],"complementary":[114],"dual":[115],"id=\"M12\">\\begin{document}$":[121],"6\\ell^mp^s":[122],"id=\"M13\">\\begin{document}$":[126],"obtained.":[130]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}