{"id":"https://openalex.org/W4388107636","doi":"https://doi.org/10.1109/tit.2023.3328262","title":"MacWilliams Extension Property With Respect to Weighted Poset Metric","display_name":"MacWilliams Extension Property With Respect to Weighted Poset Metric","publication_year":2023,"publication_date":"2023-10-30","ids":{"openalex":"https://openalex.org/W4388107636","doi":"https://doi.org/10.1109/tit.2023.3328262"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2023.3328262","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2023.3328262","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/A5100462090","display_name":"Yang Xu","orcid":"https://orcid.org/0000-0003-4632-7124"},"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":true,"raw_author_name":"Yang Xu","raw_affiliation_strings":["Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-9151-8555","affiliations":[{"raw_affiliation_string":"Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai, China","institution_ids":["https://openalex.org/I24943067"]}]},{"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":["Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0003-3062-5004","affiliations":[{"raw_affiliation_string":"Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai, China","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/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"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":["Department of Mathematics, Faculty of Science, The University of Hong Kong, Hong Kong, China"],"raw_orcid":"https://orcid.org/0000-0001-9895-5646","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, The University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I200769079","https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100462090"],"corresponding_institution_ids":["https://openalex.org/I24943067"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23252942,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"70","issue":"2","first_page":"995","last_page":"1007"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9950000047683716,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9950000047683716,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9896000027656555,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/extension","display_name":"Extension (predicate logic)","score":0.806830644607544},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.7410681843757629},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.731235921382904},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6141476631164551},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5903878808021545},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48321211338043213},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.420783668756485},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3468698263168335},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3221272826194763},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2202426791191101},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06456375122070312}],"concepts":[{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.806830644607544},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.7410681843757629},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.731235921382904},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6141476631164551},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5903878808021545},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48321211338043213},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.420783668756485},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3468698263168335},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3221272826194763},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2202426791191101},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06456375122070312},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2023.3328262","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2023.3328262","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"},{"id":"pmh:oai:hub.hku.hk:10722/347738","is_oa":false,"landing_page_url":"https://hub.hku.hk/handle/10722/347738","pdf_url":null,"source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2690108622","display_name":"\u9ad8\u65af\u53cd\u9988\u5bb9\u91cf","funder_award_id":"61871343","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4310926482","display_name":null,"funder_award_id":"62272107","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G708152933","display_name":null,"funder_award_id":"17304121","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G8839316479","display_name":null,"funder_award_id":"2019YFB2101703","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G8909702553","display_name":null,"funder_award_id":"U19A2066","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/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W1606480398","https://openalex.org/W1803495500","https://openalex.org/W1972227403","https://openalex.org/W1973174922","https://openalex.org/W1975642600","https://openalex.org/W1984488462","https://openalex.org/W1984973158","https://openalex.org/W1987582100","https://openalex.org/W1994198652","https://openalex.org/W2007472708","https://openalex.org/W2010693726","https://openalex.org/W2013730723","https://openalex.org/W2024307249","https://openalex.org/W2024954696","https://openalex.org/W2031242533","https://openalex.org/W2034096494","https://openalex.org/W2043474783","https://openalex.org/W2046471908","https://openalex.org/W2067569336","https://openalex.org/W2069047683","https://openalex.org/W2079400100","https://openalex.org/W2090792284","https://openalex.org/W2101520088","https://openalex.org/W2107875783","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/W2737109129","https://openalex.org/W2754509682","https://openalex.org/W2887649350","https://openalex.org/W2922391240","https://openalex.org/W2952247110","https://openalex.org/W2962926340","https://openalex.org/W2962953446","https://openalex.org/W2963430254","https://openalex.org/W3000207348","https://openalex.org/W3014984724","https://openalex.org/W3021927480","https://openalex.org/W3099370198","https://openalex.org/W3104312933","https://openalex.org/W3214547121","https://openalex.org/W4213125419","https://openalex.org/W4225985877","https://openalex.org/W4292101331","https://openalex.org/W4293356485","https://openalex.org/W6604469142","https://openalex.org/W6636425160","https://openalex.org/W6741576075","https://openalex.org/W6758860523"],"related_works":["https://openalex.org/W2106070061","https://openalex.org/W4390961156","https://openalex.org/W1963087247","https://openalex.org/W4312224320","https://openalex.org/W2347443236","https://openalex.org/W4205203210","https://openalex.org/W2146274131","https://openalex.org/W2184328455","https://openalex.org/W2073211194","https://openalex.org/W2042560047"],"abstract_inverted_index":{"Let":[0],"<inline-formula":[1,21,33,51,60,69,82,104,114,137,150,163,173,183,205,218,242,281],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[2,22,34,52,61,70,83,105,115,138,151,164,174,184,206,219,243,282],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[3,23,35,53,62,71,84,106,116,139,152,165,175,185,207,220,244,283],"<tex-math":[4,24,36,54,63,72,85,107,117,140,153,166,176,186,208,221,245,284],"notation=\"LaTeX\">$\\mathbf":[5,64,73,118,167,177,209],"{H}$":[6,65,119,210],"</tex-math></inline-formula>":[7,26,39,57,66,77,90,110,120,143,156,169,179,189,211,224,247,287],"be":[8],"the":[9,43,101,131,147,236,262,275,303],"Cartesian":[10],"product":[11],"of":[12,15,100,103,113,136,228,238,264,270,274,277],"a":[13,19,30,79,92,98,249],"family":[14],"left":[16],"modules":[17],"over":[18],"ring":[20],"notation=\"LaTeX\">$S$":[25,246],",":[27,67,121,144],"indexed":[28],"by":[29],"finite":[31,250],"set":[32],"notation=\"LaTeX\">$\\Omega":[37],"$":[38,155,188],".":[40],"We":[41,95],"study":[42],"MacWilliams":[44,266],"extension":[45],"property":[46,134,263],"(MEP)":[47],"with":[48,193,215,230,255],"respect":[49,216,231],"to":[50,126,212,217,232],"notation=\"LaTeX\">$(\\mathbf":[55,108,141,222,285],"{P},\\omega)$":[56,109,142,223,286],"-weight":[58,111,225],"on":[59],"where":[68],"{P}=(\\Omega,\\preccurlyeq":[74],"_{\\mathbf":[75],"{P}})$":[76],"is":[78,91,123,157,170,180,190,248,298],"poset":[80],"and":[81,201,279],"notation=\"LaTeX\">$\\omega:\\Omega":[86],"\\longrightarrow":[87],"\\mathbb":[88],"{R}^{+}$":[89],"weight":[93],"function.":[94],"first":[96],"give":[97,199],"characterization":[99],"group":[102,276],"isometries":[112,278],"which":[122],"then":[124],"used":[125],"show":[127,295],"that":[128,149,162,296],"MEP":[129,214,229,254,297],"implies":[130,161],"unique":[132],"decomposition":[133],"(UDP)":[135],"which,":[145],"for":[146,204],"case":[148],"notation=\"LaTeX\">$\\omega":[154,187],"identically":[158,191],"1,":[159,192],"further":[160],"{P}$":[168,178],"hierarchical.":[171],"When":[172],"hierarchical":[181],"or":[182],"some":[194],"weak":[195],"additional":[196],"assumptions,":[197],"we":[198,252,294],"necessary":[200],"sufficient":[202],"conditions":[203],"satisfy":[213],"in":[226,292],"terms":[227],"Hamming":[233],"weight.":[234],"With":[235],"help":[237],"these":[239],"results,":[240],"when":[241],"field,":[251],"compare":[253],"various":[256],"well":[257],"studied":[258],"coding-theoretic":[259],"properties":[260],"including":[261],"admitting":[265],"identity":[267],"(PAMI),":[268],"reflexivity":[269],"partitions,":[271],"UDP,":[272],"transitivity":[273],"whether":[280],"induces":[288],"an":[289],"association":[290],"scheme;":[291],"particular,":[293],"always":[299],"stronger":[300],"than":[301],"all":[302],"other":[304],"properties.":[305]},"counts_by_year":[],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2023-11-01T00:00:00"}