{"id":"https://openalex.org/W3201703413","doi":"https://doi.org/10.3934/amc.2021044","title":"Repeated-root constacyclic codes of length 6&lt;i&gt;l&lt;sup&gt;m&lt;/sup&gt;p&lt;sup&gt;n&lt;/sup&gt;&lt;/i&gt;","display_name":"Repeated-root constacyclic codes of length 6&lt;i&gt;l&lt;sup&gt;m&lt;/sup&gt;p&lt;sup&gt;n&lt;/sup&gt;&lt;/i&gt;","publication_year":2021,"publication_date":"2021-09-27","ids":{"openalex":"https://openalex.org/W3201703413","doi":"https://doi.org/10.3934/amc.2021044","mag":"3201703413"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2021044","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2021044","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=02c9783a-ec63-4974-9495-939dc183c34e","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://www.aimsciences.org/article/exportPdf?id=02c9783a-ec63-4974-9495-939dc183c34e","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101485652","display_name":"Tingting Wu","orcid":"https://orcid.org/0000-0002-7506-5365"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tingting Wu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100613317","display_name":"Shixin Zhu","orcid":"https://orcid.org/0000-0002-2845-3568"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shixin Zhu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100418822","display_name":"Li Liu","orcid":"https://orcid.org/0000-0002-4776-5292"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li Liu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5071875723","display_name":"Lanqiang Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lanqiang Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1365,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54931755,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"17","issue":"5","first_page":"1154","last_page":"1180"},"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":0.9858999848365784,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9836999773979187,"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":0.7185915112495422},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.617713987827301},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.4444684684276581},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.44304993748664856},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3444904088973999},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32903265953063965},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16530632972717285},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12927943468093872}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7185915112495422},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.617713987827301},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.4444684684276581},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.44304993748664856},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3444904088973999},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32903265953063965},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16530632972717285},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12927943468093872},{"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/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2021044","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2021044","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=02c9783a-ec63-4974-9495-939dc183c34e","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.2021044","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2021044","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=02c9783a-ec63-4974-9495-939dc183c34e","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":16,"referenced_works":["https://openalex.org/W1594652978","https://openalex.org/W1970334168","https://openalex.org/W1973673225","https://openalex.org/W1985655855","https://openalex.org/W2014597889","https://openalex.org/W2061268162","https://openalex.org/W2143062461","https://openalex.org/W2228651896","https://openalex.org/W2345678824","https://openalex.org/W2472681438","https://openalex.org/W2795111912","https://openalex.org/W2796901457","https://openalex.org/W2964564721","https://openalex.org/W2999955196","https://openalex.org/W3030222450","https://openalex.org/W3141217652"],"related_works":["https://openalex.org/W4318195686","https://openalex.org/W2975999359","https://openalex.org/W4287173569","https://openalex.org/W2796561647","https://openalex.org/W4313513739","https://openalex.org/W3119693376","https://openalex.org/W3182422617","https://openalex.org/W2244208494","https://openalex.org/W4280497496","https://openalex.org/W2594072523"],"abstract_inverted_index":{"<p":[0],"style='text-indent:20px;'>Let":[1],"<inline-formula><tex-math":[2,12,22,36,43,48,57,72,79,95,100,108,113,141,146],"id=\"M1\">\\begin{document}$":[3],"\\mathbb{F}_{q}":[4,59,81,148],"$\\end{document}</tex-math></inline-formula>":[5,27,39,51,75,82,98,103,111,116,144],"be":[6],"a":[7,31,53],"finite":[8,77],"field":[9,78],"with":[10],"character":[11],"id=\"M2\">\\begin{document}$":[13],"p":[14],"$\\end{document}</tex-math></inline-formula>.":[15,60,149],"In":[16,120],"this":[17],"paper,":[18],"the":[19,63,65,124],"multiplicative":[20],"group":[21],"id=\"M3\">\\begin{document}$":[23],"\\mathbb{F}_{q}^{*}":[24],"=":[25],"\\mathbb{F}_{q}\\setminus\\{0\\}":[26],"is":[28,52,86],"decomposed":[29],"into":[30],"mutually":[32],"disjoint":[33],"union":[34],"of":[35,56,67,70,90,128,139],"id=\"M4\">\\begin{document}$":[37],"\\gcd(6l^mp^n,q-1)":[38],"cosets":[40],"over":[41,76,145],"subgroup":[42],"id=\"M5\">\\begin{document}$":[44],"&lt;\\xi^{6l^mp^n}&gt;":[45],"$\\end{document}</tex-math></inline-formula>,":[46],"where":[47,94],"id=\"M6\">\\begin{document}$":[49],"\\xi":[50],"primitive":[54],"element":[55],"id=\"M7\">\\begin{document}$":[58],"Based":[61],"on":[62],"decomposition,":[64],"structure":[66],"constacyclic":[68,137],"codes":[69,134,138],"length":[71,140],"id=\"M8\">\\begin{document}$":[73],"6l^mp^n":[74,143],"id=\"M9\">\\begin{document}$":[80],"and":[83,99,112,126,135],"their":[84,91],"duals":[85],"established":[87],"in":[88],"terms":[89],"generator":[92],"polynomials,":[93],"id=\"M10\">\\begin{document}$":[96],"p\\neq{3}":[97],"id=\"M11\">\\begin{document}$":[101],"l\\neq{3}":[102],"are":[104,117],"distinct":[105],"odd":[106],"primes,":[107],"id=\"M12\">\\begin{document}$":[109],"m":[110],"id=\"M13\">\\begin{document}$":[114],"n":[115],"positive":[118],"integers.":[119],"addition,":[121],"we":[122],"determine":[123],"characterization":[125],"enumeration":[127],"all":[129],"linear":[130],"complementary":[131],"dual(LCD)":[132],"negacyclic":[133],"self-dual":[136],"id=\"M14\">\\begin{document}$":[142],"id=\"M15\">\\begin{document}$":[147]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-19T21:40:30.786675","created_date":"2021-10-11T00:00:00"}