{"id":"https://openalex.org/W2115481128","doi":"https://doi.org/10.1007/s10623-009-9323-x","title":"Minimal codewords in Reed\u2013Muller codes","display_name":"Minimal codewords in Reed\u2013Muller codes","publication_year":2009,"publication_date":"2009-09-29","ids":{"openalex":"https://openalex.org/W2115481128","doi":"https://doi.org/10.1007/s10623-009-9323-x","mag":"2115481128"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-009-9323-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-009-9323-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-009-9323-x.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s10623-009-9323-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049608436","display_name":"Jeroen Schillewaert","orcid":"https://orcid.org/0000-0002-5234-1312"},"institutions":[{"id":"https://openalex.org/I185492890","display_name":"University of Canterbury","ror":"https://ror.org/03y7q9t39","country_code":"NZ","type":"education","lineage":["https://openalex.org/I185492890"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"J. Schillewaert","raw_affiliation_strings":["Mathematics and Statistics Department, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand","Mathematics and Statistics Department, University of Canterbury, Christchurch, New Zealand 8140#TAB#"],"affiliations":[{"raw_affiliation_string":"Mathematics and Statistics Department, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand","institution_ids":["https://openalex.org/I185492890"]},{"raw_affiliation_string":"Mathematics and Statistics Department, University of Canterbury, Christchurch, New Zealand 8140#TAB#","institution_ids":["https://openalex.org/I185492890"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061433215","display_name":"Leo Storme","orcid":"https://orcid.org/0000-0001-6440-9225"},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"L. Storme","raw_affiliation_strings":["Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281-S22, 9000, Ghent, Belgium","Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000"],"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281-S22, 9000, Ghent, Belgium","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000","institution_ids":["https://openalex.org/I32597200"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048746371","display_name":"J. A. Thas","orcid":"https://orcid.org/0000-0003-4577-9559"},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"J. A. Thas","raw_affiliation_strings":["Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281-S22, 9000, Ghent, Belgium","Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000"],"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281-S22, 9000, Ghent, Belgium","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000","institution_ids":["https://openalex.org/I32597200"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5049608436"],"corresponding_institution_ids":["https://openalex.org/I185492890"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.9033,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.81263166,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"54","issue":"3","first_page":"273","last_page":"286"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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/T12029","display_name":"DNA and Biological Computing","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9988999962806702,"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/reed\u2013muller-code","display_name":"Reed\u2013Muller code","score":0.6840834617614746},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.672026515007019},{"id":"https://openalex.org/keywords/secret-sharing","display_name":"Secret sharing","score":0.6224859952926636},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.6078979969024658},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5998921990394592},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5908029675483704},{"id":"https://openalex.org/keywords/weight-distribution","display_name":"Weight distribution","score":0.5884281992912292},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5188416242599487},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4966626763343811},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.49008071422576904},{"id":"https://openalex.org/keywords/binary-code","display_name":"Binary code","score":0.454393208026886},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.4474859833717346},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4227561950683594},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29172712564468384},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.25757771730422974},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2411670684814453},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.20953252911567688},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.178598552942276},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.1569545567035675},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0673743188381195}],"concepts":[{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.6840834617614746},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.672026515007019},{"id":"https://openalex.org/C3087436","wikidata":"https://www.wikidata.org/wiki/Q1386603","display_name":"Secret sharing","level":3,"score":0.6224859952926636},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6078979969024658},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5998921990394592},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5908029675483704},{"id":"https://openalex.org/C25432639","wikidata":"https://www.wikidata.org/wiki/Q3711790","display_name":"Weight distribution","level":2,"score":0.5884281992912292},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5188416242599487},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4966626763343811},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.49008071422576904},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.454393208026886},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.4474859833717346},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4227561950683594},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29172712564468384},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.25757771730422974},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2411670684814453},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.20953252911567688},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.178598552942276},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.1569545567035675},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0673743188381195},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10623-009-9323-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-009-9323-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-009-9323-x.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:archive.ugent.be:978956","is_oa":true,"landing_page_url":"http://hdl.handle.net/1854/LU-978956","pdf_url":"https://biblio.ugent.be/publication/978956/file/978961.pdf","source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0925-1022","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s10623-009-9323-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-009-9323-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-009-9323-x.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1638137056","display_name":null,"funder_award_id":"FWO-Vl","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G6867476589","display_name":null,"funder_award_id":"FWO-Vlaanderen","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2115481128.pdf","grobid_xml":"https://content.openalex.org/works/W2115481128.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W83984714","https://openalex.org/W1533708960","https://openalex.org/W1606480398","https://openalex.org/W2038242066","https://openalex.org/W2042993834","https://openalex.org/W2124113125","https://openalex.org/W2162446076","https://openalex.org/W2163834165"],"related_works":["https://openalex.org/W2920889620","https://openalex.org/W4312936811","https://openalex.org/W2952098968","https://openalex.org/W2063994293","https://openalex.org/W2161125858","https://openalex.org/W2059337883","https://openalex.org/W2134021092","https://openalex.org/W2111194052","https://openalex.org/W2033041015","https://openalex.org/W2155732318"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}