{"id":"https://openalex.org/W4285279372","doi":"https://doi.org/10.3934/amc.2022044","title":"Another expression of the MacWilliams identities and its applications","display_name":"Another expression of the MacWilliams identities and its applications","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4285279372","doi":"https://doi.org/10.3934/amc.2022044"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2022044","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2022044","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/amc.2022044","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102000741","display_name":"Fengwei Li","orcid":"https://orcid.org/0000-0002-9493-2890"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Fengwei Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109044761","display_name":"Xuemei Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xuemei Wang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102000741"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07385735,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"4","first_page":"847","last_page":"858"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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":0.9998000264167786,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9973000288009644,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9807999730110168,"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/mathematics","display_name":"Mathematics","score":0.8433834314346313},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.5911635160446167},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5222447514533997},{"id":"https://openalex.org/keywords/symbol","display_name":"Symbol (formal)","score":0.4961617887020111},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.44722169637680054},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.4353013038635254},{"id":"https://openalex.org/keywords/weight-distribution","display_name":"Weight distribution","score":0.42097264528274536},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3745616674423218},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.344396710395813},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1992570161819458},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07581883668899536},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06578567624092102}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8433834314346313},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5911635160446167},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5222447514533997},{"id":"https://openalex.org/C134400042","wikidata":"https://www.wikidata.org/wiki/Q2372244","display_name":"Symbol (formal)","level":2,"score":0.4961617887020111},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.44722169637680054},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.4353013038635254},{"id":"https://openalex.org/C25432639","wikidata":"https://www.wikidata.org/wiki/Q3711790","display_name":"Weight distribution","level":2,"score":0.42097264528274536},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3745616674423218},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.344396710395813},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1992570161819458},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07581883668899536},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06578567624092102},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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":1,"locations":[{"id":"doi:10.3934/amc.2022044","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2022044","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2022044","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2022044","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W2991581736","https://openalex.org/W3182812268","https://openalex.org/W4287101232","https://openalex.org/W4386073510","https://openalex.org/W2112972328","https://openalex.org/W2080702656","https://openalex.org/W1633971688","https://openalex.org/W4386423966","https://openalex.org/W2067569336"],"abstract_inverted_index":{"<p":[0],"style='text-indent:20px;'>Let":[1],"<inline-formula><tex-math":[2,19,55,62,70,77],"id=\"M1\">\\begin{document}$":[3],"\\mathcal":[4,64],"C":[5,65],"$\\end{document}</tex-math></inline-formula>":[6,66,75],"be":[7,38],"a":[8,16,29],"maximum":[9],"distance":[10],"separable":[11],"(MDS)":[12],"linear":[13],"code":[14],"over":[15],"finite":[17],"field":[18],"id=\"M2\">\\begin{document}$":[20],"\\Bbb":[21],"F_q":[22],"$\\end{document}</tex-math></inline-formula>.":[23],"In":[24],"this":[25],"paper,":[26],"we":[27,52],"present":[28],"new":[30,50],"formula":[31],"of":[32,43,61],"its":[33],"weight":[34,59],"distribution,":[35],"which":[36],"can":[37],"seen":[39],"as":[40],"another":[41],"expression":[42],"the":[44,49,54,68],"MacWilliams":[45],"identities.":[46],"Moreover,":[47],"using":[48],"formula,":[51],"obtain":[53],"id=\"M3\">\\begin{document}$":[56],"b":[57,72,79],"$\\end{document}</tex-math></inline-formula>-symbol":[58],"distribution":[60],"id=\"M4\">\\begin{document}$":[63],"in":[67],"cases:":[69],"id=\"M5\">\\begin{document}$":[71],"=":[73,80],"2":[74],"and":[76],"id=\"M6\">\\begin{document}$":[78],"3":[81],"$\\end{document}</tex-math></inline-formula>,":[82],"respectively.":[83]},"counts_by_year":[],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}
