{"id":"https://openalex.org/W2063618950","doi":"https://doi.org/10.1016/s0012-365x(99)00368-4","title":"Shadow lattices and shadow codes","display_name":"Shadow lattices and shadow codes","publication_year":2000,"publication_date":"2000-05-01","ids":{"openalex":"https://openalex.org/W2063618950","doi":"https://doi.org/10.1016/s0012-365x(99)00368-4","mag":"2063618950"},"language":"en","primary_location":{"id":"doi:10.1016/s0012-365x(99)00368-4","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0012-365x(99)00368-4","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0012365X99003684/pdf","source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.sciencedirect.com/science/article/pii/S0012365X99003684/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059969175","display_name":"Steven T. Dougherty","orcid":"https://orcid.org/0000-0003-4877-1923"},"institutions":[{"id":"https://openalex.org/I124113063","display_name":"University of Scranton","ror":"https://ror.org/05xwb6v37","country_code":"US","type":"education","lineage":["https://openalex.org/I124113063"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Steven T. Dougherty","raw_affiliation_strings":["Department of Mathematics, University of Scranton, Scranton, PA 18510, USA","Department of Mathematics, University of Scranton, Scranton, PA 18510, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Scranton, Scranton, PA 18510, USA","institution_ids":["https://openalex.org/I124113063"]},{"raw_affiliation_string":"Department of Mathematics, University of Scranton, Scranton, PA 18510, USA#TAB#","institution_ids":["https://openalex.org/I124113063"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015902214","display_name":"Masaaki Harada","orcid":"https://orcid.org/0000-0002-2748-6456"},"institutions":[{"id":"https://openalex.org/I112524849","display_name":"Yamagata University","ror":"https://ror.org/00xy44n04","country_code":"JP","type":"education","lineage":["https://openalex.org/I112524849"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masaaki Harada","raw_affiliation_strings":["Department of Mathematical Sciences, Yamagata University, Yamagata 990-8560, Japan","Department of Mathematical Sciences, Yamagata University,  Yamagata 990-8560, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Yamagata University, Yamagata 990-8560, Japan","institution_ids":["https://openalex.org/I112524849"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Yamagata University,  Yamagata 990-8560, Japan","institution_ids":["https://openalex.org/I112524849"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024873890","display_name":"Patrick Sol\u00e9","orcid":"https://orcid.org/0000-0002-4078-8301"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Patrick Sol\u00e9","raw_affiliation_strings":["CNRS, I3S, ESSI, BP 145, Route des Colles, 06 903 Sophia Antipolis, France","CNRS, I3S ESSI, BP 145 Route des Colles 06 903 Sophia Antipolis, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS, I3S, ESSI, BP 145, Route des Colles, 06 903 Sophia Antipolis, France","institution_ids":["https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CNRS, I3S ESSI, BP 145 Route des Colles 06 903 Sophia Antipolis, France","institution_ids":["https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5059969175"],"corresponding_institution_ids":["https://openalex.org/I124113063"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":2.2366,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.89883776,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"219","issue":"1-3","first_page":"49","last_page":"64"},"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":0.9980000257492065,"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/T11567","display_name":"semigroups and automata theory","score":0.991100013256073,"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/unimodular-matrix","display_name":"Unimodular matrix","score":0.9831962585449219},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7318153977394104},{"id":"https://openalex.org/keywords/shadow","display_name":"Shadow (psychology)","score":0.6147097945213318},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5262027382850647},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5217264890670776},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4851187467575073},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4779927134513855},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.47022581100463867},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.44575101137161255},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1637173593044281}],"concepts":[{"id":"https://openalex.org/C201958917","wikidata":"https://www.wikidata.org/wiki/Q1367055","display_name":"Unimodular matrix","level":2,"score":0.9831962585449219},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7318153977394104},{"id":"https://openalex.org/C117797892","wikidata":"https://www.wikidata.org/wiki/Q286363","display_name":"Shadow (psychology)","level":2,"score":0.6147097945213318},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5262027382850647},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5217264890670776},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4851187467575073},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4779927134513855},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.47022581100463867},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.44575101137161255},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1637173593044281},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0012-365x(99)00368-4","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0012-365x(99)00368-4","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0012365X99003684/pdf","source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/s0012-365x(99)00368-4","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0012-365x(99)00368-4","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0012365X99003684/pdf","source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.550000011920929,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2063618950.pdf","grobid_xml":"https://content.openalex.org/works/W2063618950.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W2000054582","https://openalex.org/W2003341050","https://openalex.org/W2020903930","https://openalex.org/W2022803795","https://openalex.org/W2061721328","https://openalex.org/W2114751427","https://openalex.org/W2127017001","https://openalex.org/W2127123421","https://openalex.org/W2143295365","https://openalex.org/W2151813678","https://openalex.org/W2152441705","https://openalex.org/W2158848893","https://openalex.org/W2177092276","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2011745869","https://openalex.org/W2088028898","https://openalex.org/W2950905816","https://openalex.org/W211627054","https://openalex.org/W1608437562","https://openalex.org/W2083668208","https://openalex.org/W3141916192","https://openalex.org/W2171197936","https://openalex.org/W2094499544","https://openalex.org/W2062949095"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}
