{"id":"https://openalex.org/W4221154830","doi":"https://doi.org/10.1109/isit50566.2022.9834442","title":"Minimal Length of Nontrivial Solutions of the Isometry Equation and MacWilliams Extension Property with Respect to Weighted Poset Metric","display_name":"Minimal Length of Nontrivial Solutions of the Isometry Equation and MacWilliams Extension Property with Respect to Weighted Poset Metric","publication_year":2022,"publication_date":"2022-06-26","ids":{"openalex":"https://openalex.org/W4221154830","doi":"https://doi.org/10.1109/isit50566.2022.9834442"},"language":"en","primary_location":{"id":"doi:10.1109/isit50566.2022.9834442","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit50566.2022.9834442","pdf_url":null,"source":{"id":"https://openalex.org/S4363604560","display_name":"2022 IEEE International Symposium on Information Theory (ISIT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-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/A5100855152","display_name":"Yang Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["CN","HK"],"is_corresponding":true,"raw_author_name":"Yang Xu","raw_affiliation_strings":["Fudan University,Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science","Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University","Department of Mathematics, The University of Hong Kong"],"affiliations":[{"raw_affiliation_string":"Fudan University,Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Department of Mathematics, The University of Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025009140","display_name":"Haibin Kan","orcid":"https://orcid.org/0000-0003-3062-5004"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haibin Kan","raw_affiliation_strings":["Fudan University,Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science","Shanghai Engineering Research Center of Blockchain, Yiwu Research Institute of Fudan University","Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University"],"affiliations":[{"raw_affiliation_string":"Fudan University,Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Shanghai Engineering Research Center of Blockchain, Yiwu Research Institute of Fudan University","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000081781","display_name":"Guangyue Han","orcid":"https://orcid.org/0000-0001-9895-5646"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Guangyue Han","raw_affiliation_strings":["The University of Hong Kong,Department of Mathematics","Department of Mathematics, The University of Hong Kong"],"affiliations":[{"raw_affiliation_string":"The University of Hong Kong,Department of Mathematics","institution_ids":["https://openalex.org/I177725633","https://openalex.org/I889458895"]},{"raw_affiliation_string":"Department of Mathematics, The University of Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100855152"],"corresponding_institution_ids":["https://openalex.org/I24943067","https://openalex.org/I889458895"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01851852,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1969","last_page":"1974"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/isometry","display_name":"Isometry (Riemannian geometry)","score":0.6786034107208252},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6233479976654053},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45406055450439453},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4255450963973999},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19123563170433044}],"concepts":[{"id":"https://openalex.org/C82457910","wikidata":"https://www.wikidata.org/wiki/Q740207","display_name":"Isometry (Riemannian geometry)","level":2,"score":0.6786034107208252},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6233479976654053},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45406055450439453},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4255450963973999},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19123563170433044}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit50566.2022.9834442","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit50566.2022.9834442","pdf_url":null,"source":{"id":"https://openalex.org/S4363604560","display_name":"2022 IEEE International Symposium on Information Theory (ISIT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"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":35,"referenced_works":["https://openalex.org/W1803495500","https://openalex.org/W1972841274","https://openalex.org/W1973174922","https://openalex.org/W1975642600","https://openalex.org/W1984488462","https://openalex.org/W1994198652","https://openalex.org/W2010693726","https://openalex.org/W2013730723","https://openalex.org/W2024307249","https://openalex.org/W2024954696","https://openalex.org/W2031242533","https://openalex.org/W2043474783","https://openalex.org/W2109684601","https://openalex.org/W2153567880","https://openalex.org/W2171812691","https://openalex.org/W2265285816","https://openalex.org/W2285899034","https://openalex.org/W2540057585","https://openalex.org/W2547936968","https://openalex.org/W2601579928","https://openalex.org/W2754509682","https://openalex.org/W2887649350","https://openalex.org/W2918466505","https://openalex.org/W2922391240","https://openalex.org/W2952247110","https://openalex.org/W2962926340","https://openalex.org/W2962953446","https://openalex.org/W2963430254","https://openalex.org/W3021927480","https://openalex.org/W3099370198","https://openalex.org/W3104312933","https://openalex.org/W4225985877","https://openalex.org/W4293356485","https://openalex.org/W6636425160","https://openalex.org/W6758860523"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"For":[0,109,160],"$R":[1],"\\triangleq":[2,26,115],"Ma{t_m}({\\mathbb{F}})$,":[3],"the":[4,13,22,36,42,53,65,90,95,102,110,144,166,169,183,202,205],"ring":[5],"of":[6,39,41,98,101,179],"all":[7],"m":[8,10,29],"\u00d7":[9],"matrices":[11],"over":[12],"finite":[14,107,111],"field":[15],"${\\mathbb{F}}$":[16],"with":[17,28,70,204,222],"$|{\\mathbb{F}}|":[18],"=":[19,79,124],"q$,":[20],"and":[21,131,156,171,182,195,236],"left":[23],"R-module":[24],"$A":[25],"Ma{t_{m,k}}({\\mathbb{F}})$":[27],"+":[30,83],"1":[31],"\u2a7d":[32],"k,":[33],"by":[34,153,234],"deriving":[35],"minimal":[37,54,96],"length":[38,56,97],"solutions":[40,100],"related":[43],"isometry":[44,103],"equation,":[45],"Dyshko":[46],"has":[47,150],"proved":[48],"in":[49,158,238],"[3],":[50],"[4]":[51],"that":[52,208],"code":[55],"n":[57],"for":[58,105,189,198],"A":[59],"<sup":[60,138],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[61,128,139],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[62],"not":[63],"satisfying":[64],"MacWilliams":[66,176],"extension":[67],"property":[68],"(MEP)":[69],"respect":[71],"to":[72,77,143,200,228],"Hamming":[73],"weight":[74],"is":[75,211,215],"equal":[76],"$\\prod\\nolimits_{i":[78],"1}^m":[80],"{\\left(":[81],"{{q^i}":[82],"1}":[84],"\\right)}$.":[85],"In":[86],"this":[87],"paper,":[88],"using":[89],"M\u00f6bius":[91],"functions,":[92],"we":[93,164],"derive":[94],"nontrivial":[99],"equation":[104],"a":[106,121,132,162,231],"lattice.":[108],"vector":[112],"space":[113],"${\\mathbf{H}}":[114],"\\prod\\nolimits_{i":[116],"\\in":[117],"\\Omega":[118],"}":[119],"{{{\\mathbb{F}}^{{k_i}}}}$,":[120],"poset":[122],"P":[123,210],"(\u03a9,":[125],"\u227c":[126],"<inf":[127],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">P</inf>":[129],")":[130],"map":[133],"\u03c9:":[134],"\u03a9":[135],"\u2192":[136],"\u211d":[137],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">+</sup>":[140],"give":[141,193],"rise":[142],"(P,":[145,190,219],"\u03c9)-weight":[146,220],"on":[147],"H,":[148],"which":[149,224],"been":[151],"proposed":[152,233],"Hyun,":[154],"Kim":[155],"Park":[157],"[18].":[159],"such":[161],"weight,":[163],"study":[165],"relations":[167],"between":[168],"MEP":[170,203],"other":[172],"properties":[173],"including":[174],"admitting":[175],"identity,":[177],"Fourier-reflexivity":[178],"involved":[180],"partitions":[181],"Unique":[184],"Decomposition":[185],"Property":[186],"(UDP)":[187],"defined":[188],"\u03c9).":[191],"We":[192],"necessary":[194],"sufficient":[196],"conditions":[197],"H":[199],"satisfy":[201],"additional":[206],"assumption":[207],"either":[209],"hierarchical":[212],"or":[213],"\u03c9":[214],"identically":[216],"1,":[217],"i.e.,":[218],"coincides":[221],"P-weight,":[223],"further":[225],"allow":[226],"us":[227],"partly":[229],"answer":[230],"conjecture":[232],"Machado":[235],"Firer":[237],"[22].":[239]},"counts_by_year":[],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2022-04-03T00:00:00"}