{"id":"https://openalex.org/W4411856488","doi":"https://doi.org/10.3934/math.2025681","title":"Equivalence of constacyclic codes over finite non-chain ring and quantum codes","display_name":"Equivalence of constacyclic codes over finite non-chain ring and quantum codes","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4411856488","doi":"https://doi.org/10.3934/math.2025681"},"language":"en","primary_location":{"id":"doi:10.3934/math.2025681","doi":"https://doi.org/10.3934/math.2025681","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.2025681","pdf_url":"http://www.aimspress.com/aimspress-data/math/2025/7/PDF/math-10-07-681.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","poland-20","russia-white-list-1","vabb-shw"],"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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://www.aimspress.com/aimspress-data/math/2025/7/PDF/math-10-07-681.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100454239","display_name":"Jie Liu","orcid":"https://orcid.org/0009-0005-1086-3605","observed_orcids":["https://orcid.org/0009-0005-1086-3605"]},"institutions":[{"id":"https://openalex.org/I92092256","display_name":"Huanghe Science and Technology College","ror":"https://ror.org/008p6rr25","country_code":"CN","type":"education","lineage":["https://openalex.org/I92092256"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jie Liu","raw_affiliation_strings":["Faculty of Engineering , Huanghe Science and Technology College , Zhengzhou 450063 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering , Huanghe Science and Technology College , Zhengzhou 450063 , China","institution_ids":["https://openalex.org/I92092256"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056544155","display_name":"Xiying Zheng","orcid":"https://orcid.org/0000-0003-4652-3555","observed_orcids":["https://orcid.org/0000-0003-4652-3555"]},"institutions":[{"id":"https://openalex.org/I92092256","display_name":"Huanghe Science and Technology College","ror":"https://ror.org/008p6rr25","country_code":"CN","type":"education","lineage":["https://openalex.org/I92092256"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiying Zheng","raw_affiliation_strings":["Faculty of Engineering, Huanghe Science and Technology College, Zhengzhou 450063, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Huanghe Science and Technology College, Zhengzhou 450063, China","institution_ids":["https://openalex.org/I92092256"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I92092256"],"apc_list":{"value":1200,"currency":"USD","value_usd":1200},"apc_paid":{"value":1200,"currency":"USD","value_usd":1200},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11014945,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"7","first_page":"15193","last_page":"15205"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9984999895095825,"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":0.9984999895095825,"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":0.00019999999494757503,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/constacyclic-codes","display_name":"constacyclic codes","score":1.0},{"id":"https://openalex.org/keywords/isometries","display_name":"isometries","score":0.5360000133514404},{"id":"https://openalex.org/keywords/code-equivalence","display_name":"code equivalence","score":0.9380000233650208},{"id":"https://openalex.org/keywords/css-construction","display_name":"CSS construction","score":0.7350000143051147},{"id":"https://openalex.org/keywords/quantum-error-correcting-codes","display_name":"quantum error-correcting codes","score":0.8980000019073486},{"id":"https://openalex.org/keywords/code-classification","display_name":"code classification","score":0.6179999709129333}],"concepts":[{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6371562480926514},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.5132174491882324},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5126677751541138},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5099836587905884},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4987196922302246},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44028523564338684},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3645031452178955},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2754749059677124},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10921993851661682},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.08709046244621277},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/math.2025681","doi":"https://doi.org/10.3934/math.2025681","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.2025681","pdf_url":"http://www.aimspress.com/aimspress-data/math/2025/7/PDF/math-10-07-681.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","poland-20","russia-white-list-1","vabb-shw"],"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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d2612cc5fbd844aeb611ccc8583af90d","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/d2612cc5fbd844aeb611ccc8583af90d","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,"listed_in":[],"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":"AIMS Mathematics, Vol 10, Iss 7, Pp 15193-15205 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/math.2025681","doi":"https://doi.org/10.3934/math.2025681","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.2025681","pdf_url":"http://www.aimspress.com/aimspress-data/math/2025/7/PDF/math-10-07-681.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","poland-20","russia-white-list-1","vabb-shw"],"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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411856488.pdf","grobid_xml":"https://content.openalex.org/works/W4411856488.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1598308149","https://openalex.org/W1994198652","https://openalex.org/W2061268162","https://openalex.org/W2099693138","https://openalex.org/W2519564756","https://openalex.org/W2560746398","https://openalex.org/W2889940767","https://openalex.org/W3048314702","https://openalex.org/W3082887303","https://openalex.org/W4280570308","https://openalex.org/W4295533041","https://openalex.org/W4296311596","https://openalex.org/W4317212657","https://openalex.org/W4319264042","https://openalex.org/W4385504827","https://openalex.org/W4390500070","https://openalex.org/W4403537272","https://openalex.org/W4404700520"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W3123455607","https://openalex.org/W2487240277","https://openalex.org/W4210262480","https://openalex.org/W3097860111","https://openalex.org/W2138137818","https://openalex.org/W1978471113","https://openalex.org/W2505610287","https://openalex.org/W4287830728","https://openalex.org/W2060892772"],"abstract_inverted_index":{"Let":[0],"$":[1,12,17,19,24,29,42,52,57,72,84,86],"\\mathfrak":[2],"{R}_{l}":[3],"=":[4,14],"{\\mathbb":[5],"F}_{q}[u]/":[6],"\\langle":[7],"u^{l}-u":[8],"\\rangle":[9],"$,":[10,16,28,44],"where":[11],"q":[13],"p^m":[15],"p":[18],"is":[20],"a":[21],"prime,":[22],"and":[23,36,45,56,87],"m":[25],"\\in":[26],"\\mathbf{N^+}":[27],"(l-1)\\mid(p-1)":[30],"$.":[31,74],"First,":[32],"we":[33,46,67,90],"study":[34],"isometry":[35],"equivalence":[37,49,65,79],"between":[38],"constacyclic":[39,69,81],"codes":[40,70,82,95,102],"over":[41,71,83],"\\mathfrak{R}_{l}":[43,73,85],"present":[47],"the":[48,64,78,100],"conditions":[50],"for":[51],"(e_1a_1+e_2a_2+\\cdots+e_{l}a_{l})":[53],"$-constacyclic":[54,59],"code":[55],"(e_1b_1+e_2b_2+\\cdots+e_{l}b_{l})":[58],"code.":[60],"Further,":[61],"based":[62,76],"on":[63,77],"conditions,":[66],"classify":[68],"Finally,":[75],"of":[80],"CSS":[88],"construction,":[89],"construct":[91],"some":[92,104],"new":[93],"quantum":[94],"that":[96],"are":[97],"better":[98],"than":[99],"existing":[101],"in":[103],"recent":[105],"references.":[106]},"counts_by_year":[],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}
