{"id":"https://openalex.org/W2159989009","doi":"https://doi.org/10.1007/s11424-015-2246-x","title":"Macwilliams identities of linear codes over the ring F 2 + uF 2 + vF 2","display_name":"Macwilliams identities of linear codes over the ring F 2 + uF 2 + vF 2","publication_year":2015,"publication_date":"2015-04-29","ids":{"openalex":"https://openalex.org/W2159989009","doi":"https://doi.org/10.1007/s11424-015-2246-x","mag":"2159989009"},"language":"en","primary_location":{"id":"doi:10.1007/s11424-015-2246-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-015-2246-x","pdf_url":null,"source":{"id":"https://openalex.org/S45848134","display_name":"Journal of Systems Science and Complexity","issn_l":"1009-6124","issn":["1009-6124","1559-7067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Systems Science and Complexity","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/A5041737823","display_name":"Xiusheng Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210122157","display_name":"Hubei Polytechnic University","ror":"https://ror.org/01z07eq06","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210122157"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiusheng Liu","raw_affiliation_strings":["School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, 435003, China","School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, 435003, China","institution_ids":["https://openalex.org/I4210122157"]},{"raw_affiliation_string":"School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, China","institution_ids":["https://openalex.org/I4210122157"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050393369","display_name":"Hualu Liu","orcid":"https://orcid.org/0000-0002-9785-8294"},"institutions":[{"id":"https://openalex.org/I4210122157","display_name":"Hubei Polytechnic University","ror":"https://ror.org/01z07eq06","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210122157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hualu Liu","raw_affiliation_strings":["School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, 435003, China","School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, 435003, China","institution_ids":["https://openalex.org/I4210122157"]},{"raw_affiliation_string":"School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, China","institution_ids":["https://openalex.org/I4210122157"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5041737823"],"corresponding_institution_ids":["https://openalex.org/I4210122157"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.4365,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.7697587,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"28","issue":"3","first_page":"691","last_page":"701"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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":0.9973999857902527,"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/T10849","display_name":"Finite Group Theory Research","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/hamming-code","display_name":"Hamming code","score":0.8023887872695923},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6306249499320984},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.5946677923202515},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.5749877691268921},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5518067479133606},{"id":"https://openalex.org/keywords/hamming-weight","display_name":"Hamming weight","score":0.5419330596923828},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5130513906478882},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.5068045258522034},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48761311173439026},{"id":"https://openalex.org/keywords/weight-function","display_name":"Weight function","score":0.44549232721328735},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.1965378224849701},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14930981397628784},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06921935081481934},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.06565377116203308}],"concepts":[{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.8023887872695923},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6306249499320984},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.5946677923202515},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5749877691268921},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5518067479133606},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.5419330596923828},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5130513906478882},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.5068045258522034},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48761311173439026},{"id":"https://openalex.org/C134466208","wikidata":"https://www.wikidata.org/wiki/Q1520657","display_name":"Weight function","level":2,"score":0.44549232721328735},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.1965378224849701},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14930981397628784},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06921935081481934},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.06565377116203308},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11424-015-2246-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-015-2246-x","pdf_url":null,"source":{"id":"https://openalex.org/S45848134","display_name":"Journal of Systems Science and Complexity","issn_l":"1009-6124","issn":["1009-6124","1559-7067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Systems Science and Complexity","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":12,"referenced_works":["https://openalex.org/W1973174922","https://openalex.org/W2031685689","https://openalex.org/W2038681062","https://openalex.org/W2054795976","https://openalex.org/W2114972298","https://openalex.org/W2124980282","https://openalex.org/W2393139824","https://openalex.org/W2406976870","https://openalex.org/W2912167936","https://openalex.org/W2914855067","https://openalex.org/W4249397549","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2008960744","https://openalex.org/W2105471374","https://openalex.org/W2963549154","https://openalex.org/W2158117886","https://openalex.org/W1987803429","https://openalex.org/W1582340598","https://openalex.org/W1519122282","https://openalex.org/W1530654122","https://openalex.org/W2182731056","https://openalex.org/W2176368139"],"abstract_inverted_index":null,"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-01-15T23:16:33.117629","created_date":"2025-10-10T00:00:00"}