{"id":"https://openalex.org/W4408442333","doi":"https://doi.org/10.1109/tit.2025.3550982","title":"On the MacWilliams Theorem Over Codes and Lattices","display_name":"On the MacWilliams Theorem Over Codes and Lattices","publication_year":2025,"publication_date":"2025-03-14","ids":{"openalex":"https://openalex.org/W4408442333","doi":"https://doi.org/10.1109/tit.2025.3550982"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2025.3550982","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3550982","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/A5112730556","display_name":"Zhiyong Zheng","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhiyong Zheng","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University, Beijing, China","Tsinghua university, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Tsinghua university, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028512378","display_name":"Fengxia Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I2799850029","display_name":"Dongguan University of Technology","ror":"https://ror.org/01m8p7q42","country_code":"CN","type":"education","lineage":["https://openalex.org/I2799850029"]},{"id":"https://openalex.org/I78988378","display_name":"Renmin University of China","ror":"https://ror.org/041pakw92","country_code":"CN","type":"education","lineage":["https://openalex.org/I78988378"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fengxia Liu","raw_affiliation_strings":["Research Center for Mathematics and Information Security, Great Bay University, Dongguan, China","Engineering Research Center of Ministry of Education for Financial Computing and Digital Engineering, Renmin University of China, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-3098-3533","affiliations":[{"raw_affiliation_string":"Research Center for Mathematics and Information Security, Great Bay University, Dongguan, China","institution_ids":["https://openalex.org/I2799850029"]},{"raw_affiliation_string":"Engineering Research Center of Ministry of Education for Financial Computing and Digital Engineering, Renmin University of China, Beijing, China","institution_ids":["https://openalex.org/I78988378"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064260698","display_name":"Kun Tian","orcid":"https://orcid.org/0000-0003-0271-1036"},"institutions":[{"id":"https://openalex.org/I2799850029","display_name":"Dongguan University of Technology","ror":"https://ror.org/01m8p7q42","country_code":"CN","type":"education","lineage":["https://openalex.org/I2799850029"]},{"id":"https://openalex.org/I78988378","display_name":"Renmin University of China","ror":"https://ror.org/041pakw92","country_code":"CN","type":"education","lineage":["https://openalex.org/I78988378"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kun Tian","raw_affiliation_strings":["Research Center for Mathematics and Information Security, Great Bay University, Dongguan, China","Engineering Research Center of Ministry of Education for Financial Computing and Digital Engineering, Renmin University of China, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-0271-1036","affiliations":[{"raw_affiliation_string":"Research Center for Mathematics and Information Security, Great Bay University, Dongguan, China","institution_ids":["https://openalex.org/I2799850029"]},{"raw_affiliation_string":"Engineering Research Center of Ministry of Education for Financial Computing and Digital Engineering, Renmin University of China, Beijing, China","institution_ids":["https://openalex.org/I78988378"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5112730556"],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05590822,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"71","issue":"5","first_page":"3560","last_page":"3568"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11567","display_name":"semigroups and automata theory","score":0.9858999848365784,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9684000015258789,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.47951701283454895},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4677937626838684},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37626922130584717}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47951701283454895},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4677937626838684},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37626922130584717}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2025.3550982","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3550982","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W342179737","https://openalex.org/W1471103927","https://openalex.org/W1966250211","https://openalex.org/W1971488652","https://openalex.org/W1972050218","https://openalex.org/W1980508832","https://openalex.org/W1985479500","https://openalex.org/W1994790157","https://openalex.org/W1995728465","https://openalex.org/W2021208048","https://openalex.org/W2037426925","https://openalex.org/W2040009340","https://openalex.org/W2054811189","https://openalex.org/W2071740498","https://openalex.org/W2082314545","https://openalex.org/W2089419199","https://openalex.org/W2106396284","https://openalex.org/W2123797809","https://openalex.org/W2127558904","https://openalex.org/W2129571642","https://openalex.org/W2889940767","https://openalex.org/W2974889382","https://openalex.org/W4226172654","https://openalex.org/W4233469339","https://openalex.org/W4236587233","https://openalex.org/W4293259454"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","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"],"abstract_inverted_index":{"Analogies":[0],"between":[1],"codes":[2],"and":[3],"lattices":[4],"have":[5],"been":[6],"extensively":[7],"studied":[8],"for":[9],"the":[10,16,20,24,29,34,38,47,55,61,74,78,82],"last":[11],"decades.":[12],"In":[13,59,77],"this":[14,101],"context,":[15],"MacWilliams":[17,42,48,62,85],"identity":[18,86],"is":[19,44,70],"finite":[21,52],"analog":[22,53],"of":[23,28,41,54,67,80,84],"Jacobi-Poisson":[25],"summation":[26],"formula":[27],"theta":[30],"function.":[31],"Motivated":[32],"by":[33,92],"random":[35],"lattice":[36],"theory,":[37],"statistical":[39],"significance":[40],"theorem":[43],"considered.":[45],"Indeed,":[46],"distribution":[49,63],"provides":[50],"a":[51,68],"classical":[56],"Gauss":[57],"distribution.":[58,76],"particular,":[60],"over":[64],"quotient":[65],"space":[66],"code":[69],"statistically":[71],"close":[72],"to":[73,100],"uniform":[75],"context":[79],"lattices,":[81],"analogy":[83],"associated":[87],"with":[88],"nu-function":[89],"was":[90],"conjectured":[91],"Sol\u00e9":[93],"in":[94],"1995.":[95],"We":[96],"give":[97],"an":[98],"answer":[99],"problem.":[102]},"counts_by_year":[],"updated_date":"2025-12-28T23:10:05.387466","created_date":"2025-10-10T00:00:00"}