{"id":"https://openalex.org/W4396722221","doi":"https://doi.org/10.3934/amc.2024018","title":"Linear codes invariant under a linear endomorphism","display_name":"Linear codes invariant under a linear endomorphism","publication_year":2024,"publication_date":"2024-05-08","ids":{"openalex":"https://openalex.org/W4396722221","doi":"https://doi.org/10.3934/amc.2024018"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2024018","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3934/amc.2024018","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=66389da25900b55d0ecde16c","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/data/article/export-pdf?id=66389da25900b55d0ecde16c","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025041797","display_name":"Hassan Ou-azzou","orcid":"https://orcid.org/0000-0001-7401-6150"},"institutions":[{"id":"https://openalex.org/I4210153608","display_name":"Universit\u00e9 Moulay Ismail de Meknes","ror":"https://ror.org/04cnscd67","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210153608"]}],"countries":["MA"],"is_corresponding":true,"raw_author_name":"Hassan Ou-azzou","raw_affiliation_strings":["Department of Mathematics, ENSAM-Meknes Moulay Ismail University, Morocco"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, ENSAM-Meknes Moulay Ismail University, Morocco","institution_ids":["https://openalex.org/I4210153608"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057914301","display_name":"Mustapha Najmeddine","orcid":"https://orcid.org/0000-0002-4878-1219"},"institutions":[{"id":"https://openalex.org/I4210153608","display_name":"Universit\u00e9 Moulay Ismail de Meknes","ror":"https://ror.org/04cnscd67","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210153608"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Mustapha Najmeddine","raw_affiliation_strings":["Department of Mathematics, ENSAM\u2013Meknes, Moulay Ismail University, Morocco"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, ENSAM\u2013Meknes, Moulay Ismail University, Morocco","institution_ids":["https://openalex.org/I4210153608"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057272198","display_name":"Nuh Ayd\u0131n","orcid":"https://orcid.org/0000-0002-5618-2427"},"institutions":[{"id":"https://openalex.org/I166972335","display_name":"Kenyon College","ror":"https://ror.org/04ckqgs57","country_code":"US","type":"education","lineage":["https://openalex.org/I166972335"]},{"id":"https://openalex.org/I4210126612","display_name":"Azerbaijan Social Work Public Union","ror":"https://ror.org/03g93g135","country_code":"AZ","type":"nonprofit","lineage":["https://openalex.org/I4210126612"]}],"countries":["AZ","US"],"is_corresponding":false,"raw_author_name":"Nuh Aydin","raw_affiliation_strings":["Department of Mathematics, Kenyon College, Gambier, OH 43022, USA","H. OU-AZZOU,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kenyon College, Gambier, OH 43022, USA","institution_ids":["https://openalex.org/I166972335"]},{"raw_affiliation_string":"H. OU-AZZOU,","institution_ids":["https://openalex.org/I4210126612"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002521073","display_name":"Peihan Liu","orcid":"https://orcid.org/0000-0003-2403-1517"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peihan Liu","raw_affiliation_strings":["John A. Paulson School Of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02134, USA"],"affiliations":[{"raw_affiliation_string":"John A. Paulson School Of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02134, USA","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5096940291","display_name":"Brahim Ialou","orcid":null},"institutions":[{"id":"https://openalex.org/I4210153608","display_name":"Universit\u00e9 Moulay Ismail de Meknes","ror":"https://ror.org/04cnscd67","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210153608"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Brahim Ialou","raw_affiliation_strings":["Department of Mathematics, ENSAM\u2013Meknes, Moulay Ismail University, Morocco"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, ENSAM\u2013Meknes, Moulay Ismail University, Morocco","institution_ids":["https://openalex.org/I4210153608"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053076166","display_name":"El Mahdi Mouloua","orcid":null},"institutions":[{"id":"https://openalex.org/I4210153608","display_name":"Universit\u00e9 Moulay Ismail de Meknes","ror":"https://ror.org/04cnscd67","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210153608"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"El Mahdi Mouloua","raw_affiliation_strings":["Department of Mathematics, ENSAM\u2013Meknes, Moulay Ismail University, Morocco"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, ENSAM\u2013Meknes, Moulay Ismail University, Morocco","institution_ids":["https://openalex.org/I4210153608"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5025041797"],"corresponding_institution_ids":["https://openalex.org/I4210153608"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04850869,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"2","first_page":"676","last_page":"697"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9990000128746033,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9538178443908691},{"id":"https://openalex.org/keywords/endomorphism","display_name":"Endomorphism","score":0.8734997510910034},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6782640814781189},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.504848301410675},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3923704922199249},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34112516045570374},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33870038390159607},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.053405165672302246}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9538178443908691},{"id":"https://openalex.org/C116858840","wikidata":"https://www.wikidata.org/wiki/Q1340800","display_name":"Endomorphism","level":2,"score":0.8734997510910034},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6782640814781189},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.504848301410675},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3923704922199249},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34112516045570374},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33870038390159607},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.053405165672302246}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2024018","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3934/amc.2024018","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=66389da25900b55d0ecde16c","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.2024018","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3934/amc.2024018","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=66389da25900b55d0ecde16c","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4396722221.pdf"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W53349146","https://openalex.org/W1519110270","https://openalex.org/W1537824340","https://openalex.org/W1569612250","https://openalex.org/W1587885095","https://openalex.org/W1979614101","https://openalex.org/W1999121308","https://openalex.org/W2002343488","https://openalex.org/W2039541047","https://openalex.org/W2042474962","https://openalex.org/W2074084513","https://openalex.org/W2108964585","https://openalex.org/W2114207424","https://openalex.org/W2131418871","https://openalex.org/W2152669486","https://openalex.org/W2157125378","https://openalex.org/W2167413626","https://openalex.org/W2255090476","https://openalex.org/W2300646661","https://openalex.org/W2548869068","https://openalex.org/W2569339928","https://openalex.org/W2746980166","https://openalex.org/W2919050667","https://openalex.org/W3005390700","https://openalex.org/W3011673911","https://openalex.org/W3088890156","https://openalex.org/W3088895426","https://openalex.org/W3099891790","https://openalex.org/W3175712048","https://openalex.org/W4206775542","https://openalex.org/W4206960696","https://openalex.org/W4380050708","https://openalex.org/W4396793986"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4382500993","https://openalex.org/W1953984001","https://openalex.org/W4300500350","https://openalex.org/W2970062288","https://openalex.org/W2606419744","https://openalex.org/W2962902116","https://openalex.org/W2015333178","https://openalex.org/W2963415898","https://openalex.org/W2050743975"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3],"linear":[4,38,112,267],"codes":[5,39,94,113,271],"invariant":[6,40,114,240],"under":[7,41,115],"an":[8,146,151],"endomorphism":[9,21],"$":[10,12,16,48,58,68,73,78,134,142,147,152,156,158,164,166,172,197,206,210,214,218,220,226,228,235,243,253],"T,":[11],"that":[13,140],"we":[14,33,55,63,129,138,176,200,247],"call":[15,56],"T":[17],"$-codes.":[18,60],"Since":[19],"any":[20],"can":[22],"be":[23],"represented":[24],"by":[25,44,272],"a":[26,29,45,121,125,168,202],"matrix":[27,47,123,162],"when":[28],"basis":[30],"is":[31,150,236],"fixed,":[32],"shall,":[34],"for":[35,167,262],"simplicity,":[36],"consider":[37],"right":[42],"multiplication":[43],"square":[46],"M":[49,59,69,74,135,148,165,198,207,244,254],"\\in":[50],"\\mathbb{M}_{n}(":[51],"\\mathbb{F}_{_q})":[52],"$,":[53,174],"and":[54,77,95,175,209,227,256,259,268],"them":[57],"In":[61,187],"particular,":[62],"distinguish":[64],"three":[65],"fundamental":[66],"types:":[67],"$-cyclic":[70,75],"codes,":[71,76],"quasi":[72],"(M_1,":[79],"M_2,":[80],"\\dots,":[81],"M_r)":[82],"$-multi-cyclic":[83],"codes.":[84,186],"The":[85],"approach":[86],"developed":[87,276],"here":[88],"allows":[89],"us":[90,106],"to":[91,189],"realize":[92],"cyclic":[93],"many":[96],"of":[97,111,133,145,163,184,196,213,239,242,251],"their":[98],"generalizations":[99],"as":[100,120],"special":[101,117],"cases.":[102],"It":[103],"also":[104],"helps":[105],"better":[107],"understand":[108],"the":[109,131,141,160,182,194,237,249,274],"structure":[110,250],"some":[116,178],"matrices,":[118],"such":[119],"permutation":[122],"or":[124],"monomial":[126],"matrix.":[127],"Next,":[128],"study":[130,195],"duality":[132,183],"$-codes,":[136,199],"where":[137,155,219],"show":[139],"b":[143,173],"$-dual":[144],"$-code":[149],"M^{^{*}}":[153,157],"$-code,":[154],"represents":[159],"adjoint":[161],"non-degenerate":[169],"bilinear":[170],"form":[171],"explore":[177],"important":[179],"results":[180],"on":[181],"these":[185],"order":[188],"use":[190],"polynomial":[191],"rings":[192],"in":[193,277],"establish":[201],"one-to-one":[203],"correspondence":[204],"between":[205],"$-codes":[208,255],"\\mathbb{F}_{_q}[x]":[211],"$-submodules":[212],"\\prod_{i":[215],"=":[216,223],"1}^{r}R_{_{f_i}},":[217],"R_{_{f_i}}":[221],":":[222],"\\mathbb{F}_{_q}[x]/\\langle":[224],"f_{i}(x)\\rangle":[225],"(":[229],"f_{_1}(x),":[230],"f_{_{2}}(x),":[231],"\\ldots,":[232],"f_{_r}(x)":[233],")":[234],"sequence":[238],"factors":[241],"$.":[245],"Finally,":[246],"investigate":[248],"1-generator":[252],"provide":[257],"BCH-like":[258],"Hartmann-Tzeng-like":[260],"bounds":[261],"them.":[263],"We":[264],"construct":[265],"optimal":[266],"new":[269],"quantum":[270],"applying":[273],"method":[275],"this":[278],"article.":[279]},"counts_by_year":[],"updated_date":"2025-12-21T23:12:01.093139","created_date":"2025-10-10T00:00:00"}
