{"id":"https://openalex.org/W4375929133","doi":"https://doi.org/10.1109/tit.2023.3272384","title":"Roth\u2013Lempel NMDS Codes of Non-Elliptic-Curve Type","display_name":"Roth\u2013Lempel NMDS Codes of Non-Elliptic-Curve Type","publication_year":2023,"publication_date":"2023-05-08","ids":{"openalex":"https://openalex.org/W4375929133","doi":"https://doi.org/10.1109/tit.2023.3272384"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2023.3272384","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2023.3272384","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5084547874","display_name":"Dongchun Han","orcid":"https://orcid.org/0000-0002-5591-4817"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dongchun Han","raw_affiliation_strings":["School of Mathematics, Southwest Jiaotong University, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0002-5591-4817","affiliations":[{"raw_affiliation_string":"School of Mathematics, Southwest Jiaotong University, Chengdu, China","institution_ids":["https://openalex.org/I4800084"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027802106","display_name":"Cuiling Fan","orcid":"https://orcid.org/0000-0001-8467-9871"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Cuiling Fan","raw_affiliation_strings":["School of Mathematics, Southwest Jiaotong University, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0001-8467-9871","affiliations":[{"raw_affiliation_string":"School of Mathematics, Southwest Jiaotong University, Chengdu, China","institution_ids":["https://openalex.org/I4800084"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1211,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.89556664,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"69","issue":"9","first_page":"5670","last_page":"5675"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9933000206947327,"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"}},{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9919999837875366,"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/notation","display_name":"Notation","score":0.658906102180481},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5381041765213013},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.5084496736526489},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41212689876556396},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39041978120803833},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32117366790771484},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.18428662419319153},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17698505520820618},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07244211435317993}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.658906102180481},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5381041765213013},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5084496736526489},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41212689876556396},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39041978120803833},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32117366790771484},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.18428662419319153},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17698505520820618},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07244211435317993}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2023.3272384","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2023.3272384","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2612002491","display_name":null,"funder_award_id":"2682020ZT101","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G4503148698","display_name":"\u9ad8\u975e\u7ebf\u6027\u51fd\u6570\u53ca\u5176\u76f8\u5173\u7ec4\u5408\u5bf9\u8c61\u4e0e\u7f16\u7801\u7814\u7a76","funder_award_id":"11971395","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4564326132","display_name":null,"funder_award_id":"2023NSFSC0446","funder_id":"https://openalex.org/F4320329861","funder_display_name":"Natural Science Foundation of Sichuan Province"},{"id":"https://openalex.org/G4773004494","display_name":null,"funder_award_id":"2022NSFSC1856","funder_id":"https://openalex.org/F4320329861","funder_display_name":"Natural Science Foundation of Sichuan Province"},{"id":"https://openalex.org/G6328393359","display_name":null,"funder_award_id":"12231015","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8135877981","display_name":null,"funder_award_id":"12171398","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320329861","display_name":"Natural Science Foundation of Sichuan Province","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W8314386","https://openalex.org/W1202140774","https://openalex.org/W1519782116","https://openalex.org/W1530125006","https://openalex.org/W1553785754","https://openalex.org/W1557415002","https://openalex.org/W1606480398","https://openalex.org/W1977560552","https://openalex.org/W1994637991","https://openalex.org/W1997277729","https://openalex.org/W2009045150","https://openalex.org/W2023308455","https://openalex.org/W2034347399","https://openalex.org/W2041788275","https://openalex.org/W2050687505","https://openalex.org/W2131949172","https://openalex.org/W2152039952","https://openalex.org/W2162775065","https://openalex.org/W2167461394","https://openalex.org/W2901446015","https://openalex.org/W2916955409","https://openalex.org/W3022561029","https://openalex.org/W3085938014","https://openalex.org/W3119621083","https://openalex.org/W3133872036","https://openalex.org/W3144798926","https://openalex.org/W3167234496","https://openalex.org/W3178596712","https://openalex.org/W4210408507","https://openalex.org/W4292027090","https://openalex.org/W4312659204"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2504004674","https://openalex.org/W1987679298","https://openalex.org/W2963177394","https://openalex.org/W4313359513","https://openalex.org/W2498744856","https://openalex.org/W4390482104","https://openalex.org/W322408318","https://openalex.org/W149041114","https://openalex.org/W2009525028"],"abstract_inverted_index":{"The":[0],"defect":[1],"of":[2,78,83,120,134,162,176,189,221,231],"an":[3],"<inline-formula":[4,15,25,41,89,96,194,202,246],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[5,16,26,42,90,97,195,203,247],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[6,17,27,43,91,98,196,204,248],"<tex-math":[7,18,28,44,92,99,197,205,249],"notation=\"LaTeX\">$[n,k,d]$":[8],"</tex-math></inline-formula>":[9,21,31,48,94,101,199,209,252],"linear":[10,121],"code":[11,136,219,243],"is":[12,149],"defined":[13],"as":[14,124],"notation=\"LaTeX\">$s({\\mathcal{":[19,29,45],"C}})=n-k+1-d$":[20],".":[22,210,253],"Codes":[23],"with":[24,40,192],"C}})=0$":[30],"are":[32,49,85],"called":[33,50],"maximum":[34,52],"distance":[35,53],"separable":[36,54],"(MDS),":[37],"while":[38],"codes":[39,57,122,148,164,178,191,234,239],"C}})=s({\\mathcal{":[46],"C}}^{\\perp})=1$":[47],"near":[51],"(NMDS).":[55],"NMDS":[56,79,160,233,238],"correspond":[58],"to":[59,137,153,179],"interesting":[60],"objects":[61],"in":[62,69],"finite":[63],"geometry":[64],"and":[65,71,110,127,131,173,182,200,235],"have":[66,74],"nice":[67],"applications":[68],"combinatorics":[70],"cryptography.":[72],"There":[73],"been":[75],"many":[76],"constructions":[77,105],"codes,":[80,225],"but":[81],"most":[82],"them":[84],"focus":[86],"on":[87],"fixed":[88],"notation=\"LaTeX\">$q$":[93],"or":[95],"notation=\"LaTeX\">$k$":[100],",":[102],"except":[103],"for":[104,217],"from":[106],"elliptic":[107,222,236],"curves.":[108],"Roth":[109],"Lempel":[111],"(IEEE":[112],"Trans.":[113],"Inf.":[114],"Theory":[115],"1989)":[116],"constructed":[117],"a":[118],"type":[119],"(referred":[123],"Roth-Lempel":[125,135,163,177,190,232],"codes),":[126],"presented":[128],"the":[129,145,159,171,186,214,218,228],"necessary":[130,172],"sufficient":[132,174],"conditions":[133],"be":[138,166,180],"MDS.":[139],"Especially,":[140],"they":[141],"pointed":[142],"out":[143],"that":[144],"resultant":[146],"MDS":[147,224],"not":[150],"linearly":[151,229],"equivalent":[152],"Reed-Solomn":[154],"codes.":[155],"In":[156],"this":[157],"paper,":[158],"properties":[161],"will":[165],"analyzed.":[167],"We":[168],"also":[169],"obtain":[170],"condition":[175],"NMDS,":[181],"further":[183],"completely":[184],"determine":[185],"weight":[187],"distributions":[188],"length":[193],"notation=\"LaTeX\">$q+2$":[198],"dimension":[201],"notation=\"LaTeX\">$3\\leq":[206],"k\\leq":[207],"q$":[208],"Besides,":[211],"by":[212],"analyzing":[213],"upper":[215],"bound":[216],"lengths":[220,244],"curve":[223,237],"we":[226],"illustrate":[227],"inequivalence":[230],"when":[240],"their":[241],"corresponding":[242],"exceed":[245],"notation=\"LaTeX\">$4(q+2\\sqrt":[250],"{q}+1)/5+1$":[251]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":6},{"year":2023,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
