{"id":"https://openalex.org/W2032712217","doi":"https://doi.org/10.1007/s002000050051","title":"The MacWilliams theorem for two-dimensional modulo metrics","display_name":"The MacWilliams theorem for two-dimensional modulo metrics","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W2032712217","doi":"https://doi.org/10.1007/s002000050051","mag":"2032712217"},"language":"en","primary_location":{"id":"doi:10.1007/s002000050051","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002000050051","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"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":"Applicable Algebra in Engineering, Communication and Computing","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/A5103639965","display_name":"Klaus Huber","orcid":null},"institutions":[{"id":"https://openalex.org/I4210093367","display_name":"Deutsche Telekom (Germany)","ror":"https://ror.org/00m8prc86","country_code":"DE","type":"company","lineage":["https://openalex.org/I4210093367"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Klaus Huber","raw_affiliation_strings":["Deutsche Telekom AG, Forschungs- und Technologiezentrum, FZ 123a, Postfach 100003, D-64276, Darmstadt, Germany","Deutsche Telekom AG, Forschungs und Technologiezentrum, Darmstadt, Germany"],"affiliations":[{"raw_affiliation_string":"Deutsche Telekom AG, Forschungs- und Technologiezentrum, FZ 123a, Postfach 100003, D-64276, Darmstadt, Germany","institution_ids":["https://openalex.org/I4210093367"]},{"raw_affiliation_string":"Deutsche Telekom AG, Forschungs und Technologiezentrum, Darmstadt, Germany","institution_ids":["https://openalex.org/I4210093367"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5103639965"],"corresponding_institution_ids":["https://openalex.org/I4210093367"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.5444,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.62358722,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"8","issue":"1","first_page":"41","last_page":"48"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9726999998092651,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9726999998092651,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9603000283241272,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9545000195503235,"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/modulo","display_name":"Modulo","score":0.905463457107544},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49413207173347473},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4214504361152649},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41997966170310974},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3442162871360779},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28268325328826904}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.905463457107544},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49413207173347473},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4214504361152649},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41997966170310974},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3442162871360779},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28268325328826904}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s002000050051","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002000050051","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"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":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1550503464","https://openalex.org/W1594652978","https://openalex.org/W1606480398","https://openalex.org/W2153951241"],"related_works":["https://openalex.org/W2117548279","https://openalex.org/W2070252991","https://openalex.org/W2807449856","https://openalex.org/W2941201715","https://openalex.org/W2025727968","https://openalex.org/W238211858","https://openalex.org/W1979597421","https://openalex.org/W2803761277","https://openalex.org/W4297742300","https://openalex.org/W2070522125"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}