{"id":"https://openalex.org/W7116897698","doi":"https://doi.org/10.1109/tit.2025.3645262","title":"Constructions of <i>l</i> -MDS Self-Dual Codes With Flexible <i>l</i> via Deleted Generalized Reed\u2013Solomon Codes","display_name":"Constructions of <i>l</i> -MDS Self-Dual Codes With Flexible <i>l</i> via Deleted Generalized Reed\u2013Solomon Codes","publication_year":2025,"publication_date":"2025-12-23","ids":{"openalex":"https://openalex.org/W7116897698","doi":"https://doi.org/10.1109/tit.2025.3645262"},"language":null,"primary_location":{"id":"doi:10.1109/tit.2025.3645262","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3645262","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/A5103162210","display_name":"Ruhao Wan","orcid":"https://orcid.org/0000-0002-8717-020X"},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ruhao Wan","raw_affiliation_strings":["School of Mathematics, Hefei University of Technology, Hefei, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Hefei University of Technology, Hefei, China","institution_ids":["https://openalex.org/I16365422"]}]},{"author_position":"last","author":{"id":null,"display_name":"Shixin Zhu","orcid":"https://orcid.org/0000-0002-2845-3568"},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shixin Zhu","raw_affiliation_strings":["School of Mathematics, Hefei University of Technology, Hefei, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Hefei University of Technology, Hefei, China","institution_ids":["https://openalex.org/I16365422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103162210"],"corresponding_institution_ids":["https://openalex.org/I16365422"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.80623182,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"2","first_page":"961","last_page":"984"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9860000014305115,"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":0.9860000014305115,"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":0.004999999888241291,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.0015999999595806003,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/weight-distribution","display_name":"Weight distribution","score":0.5002999901771545},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.4837999939918518},{"id":"https://openalex.org/keywords/combinatorial-design","display_name":"Combinatorial design","score":0.45419999957084656},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4368000030517578},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.42660000920295715},{"id":"https://openalex.org/keywords/expander-code","display_name":"Expander code","score":0.41769999265670776},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.4052000045776367},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.40209999680519104},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.3799999952316284}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5666999816894531},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5309000015258789},{"id":"https://openalex.org/C25432639","wikidata":"https://www.wikidata.org/wiki/Q3711790","display_name":"Weight distribution","level":2,"score":0.5002999901771545},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.4837999939918518},{"id":"https://openalex.org/C122451846","wikidata":"https://www.wikidata.org/wiki/Q5150824","display_name":"Combinatorial design","level":2,"score":0.45419999957084656},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4368000030517578},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.42660000920295715},{"id":"https://openalex.org/C108509264","wikidata":"https://www.wikidata.org/wiki/Q5420758","display_name":"Expander code","level":5,"score":0.41769999265670776},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40720000863075256},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.4052000045776367},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.40209999680519104},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.3799999952316284},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.3652999997138977},{"id":"https://openalex.org/C3087436","wikidata":"https://www.wikidata.org/wiki/Q1386603","display_name":"Secret sharing","level":3,"score":0.36000001430511475},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.3495999872684479},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34599998593330383},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3158000111579895},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.3091000020503998},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.30250000953674316},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.2996000051498413},{"id":"https://openalex.org/C3427991","wikidata":"https://www.wikidata.org/wiki/Q651426","display_name":"Group code","level":5,"score":0.29910001158714294},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.296999990940094},{"id":"https://openalex.org/C128151799","wikidata":"https://www.wikidata.org/wiki/Q13563306","display_name":"Luby transform code","level":5,"score":0.2912999987602234},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C65058987","wikidata":"https://www.wikidata.org/wiki/Q7826005","display_name":"Tornado code","level":5,"score":0.27000001072883606},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.26089999079704285},{"id":"https://openalex.org/C114504821","wikidata":"https://www.wikidata.org/wiki/Q2164281","display_name":"Turbo code","level":3,"score":0.25859999656677246}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2025.3645262","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3645262","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/G1853049553","display_name":null,"funder_award_id":"U21A20428","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3478839853","display_name":null,"funder_award_id":"12171134","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1530125006","https://openalex.org/W1993275030","https://openalex.org/W2046947513","https://openalex.org/W2101288164","https://openalex.org/W2121387622","https://openalex.org/W2148402917","https://openalex.org/W2152039952","https://openalex.org/W2284727451","https://openalex.org/W2576159841","https://openalex.org/W2742143639","https://openalex.org/W2782355587","https://openalex.org/W2791809676","https://openalex.org/W2901446015","https://openalex.org/W2936252904","https://openalex.org/W2941818581","https://openalex.org/W2945051308","https://openalex.org/W2951417062","https://openalex.org/W2963610864","https://openalex.org/W2997291310","https://openalex.org/W3008782537","https://openalex.org/W3083307195","https://openalex.org/W3132613122","https://openalex.org/W3166709961","https://openalex.org/W3167143870","https://openalex.org/W3178596712","https://openalex.org/W3206988893","https://openalex.org/W4205233257","https://openalex.org/W4205400258","https://openalex.org/W4206775542","https://openalex.org/W4207062140","https://openalex.org/W4239704585","https://openalex.org/W4285173758","https://openalex.org/W4292408570","https://openalex.org/W4360993803","https://openalex.org/W4383822117","https://openalex.org/W4386597616","https://openalex.org/W4387721160","https://openalex.org/W4388654496","https://openalex.org/W4392193942","https://openalex.org/W4400590759"],"related_works":[],"abstract_inverted_index":{"<italic":[0,111,118,127,134,140,145,148,207,218,222,244,251,257,261,267,275,290,297],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[1,112,114,116,119,121,128,135,141,143,146,149,208,219,223,245,252,258,262,264,268,276,284,288,291,298],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">l</i>-MDS":[2,209,246,292],"codes,":[3,11,61,79,185,214,236],"as":[4],"a":[5,53,203,216],"generalization":[6],"of":[7,18,55,57,67,96,159,169,183,233,243],"MDS":[8,234],"and":[9,29,39,42,59,75,80,104,126,139,189],"NMDS":[10],"have":[12,43],"wide":[13],"applications":[14],"in":[15,46],"the":[16,92,97,108,156,160,166,170,179,229],"areas":[17],"secret":[19],"sharing":[20],"schemes,":[21],"index":[22],"coding":[23,27],"problems,":[24],"informed":[25],"source":[26],"problems":[28],"combinatorial":[30],"designs.":[31],"Self-dual":[32],"codes":[33,69,74,99,194,211,248,294],"are":[34],"closely":[35],"related":[36],"to":[37],"combinatorics":[38],"lattice":[40],"theory":[41],"important":[44],"application":[45],"cryptography.":[47],"In":[48,131,254],"this":[49],"paper,":[50],"by":[51],"considering":[52],"class":[54],"subcodes":[56],"GRS":[58,72,181],"EGRS":[60],"we":[62,88,153,164,175,201,237],"introduce":[63],"two":[64],"new":[65,241],"classes":[66,242],"linear":[68],"termed":[70],"deleted":[71],"(DGRS)":[73],"extended":[76],"DGRS":[77,98,161,171,184,193,213],"(EDGRS)":[78],"demonstrate":[81],"their":[82],"equivalence":[83],"under":[84],"certain":[85],"conditions.":[86],"Firstly,":[87],"not":[89,176],"only":[90,177],"determine":[91,155],"parity":[93],"check":[94],"matrix":[95],"but":[100,186],"also":[101],"give":[102,165,187],"sufficient":[103,188],"necessary":[105,190],"conditions":[106,191],"for":[107,192,205,215],"Singleton":[109],"defect":[110],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">S</i>(<italic":[113],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">C<sub>k</sub></i>(<italic":[115,142],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">a</i>,":[117,144],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">v</i>,<italic":[120],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">h</i>))":[122],"=":[123,137,260],"0,":[124],"1":[125,138,271],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">l</i>,":[129],"respectively.":[130],"particular,":[132,255],"if":[133,256],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">l</i>":[136,220,299],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">v</i>,":[147],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">h</i>)":[150],"is":[151],"NMDS,":[152],"can":[154,300],"weight":[157],"distribution":[158],"codes.":[162,172],"Furthermore,":[163],"Schur":[167],"square":[168],"From":[173],"this,":[174],"obtain":[178],"non-":[180],"properties":[182],"be":[195,301],"self-orthogonal":[196],"or":[197],"(almost)":[198],"self-dual.":[199],"Finally,":[200],"present":[202],"criterion":[204],"constructing":[206],"self-dual":[210,235,247,293],"via":[212],"given":[217],"\u2264":[221],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</i>/2":[224],"\u22122.":[225],"Then":[226],"based":[227],"on":[228],"currently":[230],"known":[231],"constructions":[232],"explicitly":[238],"construct":[239],"many":[240],"with":[249,295],"flexible":[250,296],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">l</i>.":[253],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q</i>":[259],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">r</i><sup":[263],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>,":[265],"where":[266],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">r</i>":[269,277],"\u2261":[270,278],"(mod":[272,280],"4)":[273],"(resp.":[274,286],"3":[279],"4)),":[281],"about":[282],"23<italic":[283],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q</i>%":[285],"27<italic":[287],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q</i>%)":[289],"constructed.":[302]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-12-23T00:00:00"}