{"id":"https://openalex.org/W1590335557","doi":"https://doi.org/10.37236/1489","title":"Linear Codes over Finite Chain Rings","display_name":"Linear Codes over Finite Chain Rings","publication_year":1999,"publication_date":"1999-12-18","ids":{"openalex":"https://openalex.org/W1590335557","doi":"https://doi.org/10.37236/1489","mag":"1590335557"},"language":"en","primary_location":{"id":"doi:10.37236/1489","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1489","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r11/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r11/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086666884","display_name":"Thomas Honold","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]},{"id":"https://openalex.org/I4210129716","display_name":"Maroc Numeric Cluster","ror":"https://ror.org/03q98b746","country_code":"MA","type":"other","lineage":["https://openalex.org/I4210129716"]}],"countries":["DE","MA"],"is_corresponding":true,"raw_author_name":"Thomas Honold","raw_affiliation_strings":["Zentrum Mathematik Technische Universitt Mnchen D-80290 Mnchen, Germany","Zentrum Mathematik Technische Universit\u00e4t M\u00fcnchen D-80290 M\u00fcnchen, Germany"],"affiliations":[{"raw_affiliation_string":"Zentrum Mathematik Technische Universitt Mnchen D-80290 Mnchen, Germany","institution_ids":["https://openalex.org/I4210129716"]},{"raw_affiliation_string":"Zentrum Mathematik Technische Universit\u00e4t M\u00fcnchen D-80290 M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076168644","display_name":"Ivan Landjev","orcid":"https://orcid.org/0000-0001-5147-5186"},"institutions":[{"id":"https://openalex.org/I24768866","display_name":"Bulgarian Academy of Sciences","ror":"https://ror.org/01x8hew03","country_code":"BG","type":"funder","lineage":["https://openalex.org/I24768866"]},{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Ivan Landjev","raw_affiliation_strings":["Institute of Mathematics and Informatics Bulgarian Academy of Sciences 8 Acad. G. Bonchev str. 1113 Sofia, Bulgaria"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Informatics Bulgarian Academy of Sciences 8 Acad. G. Bonchev str. 1113 Sofia, Bulgaria","institution_ids":["https://openalex.org/I4210105926","https://openalex.org/I24768866"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086666884"],"corresponding_institution_ids":["https://openalex.org/I4210129716","https://openalex.org/I62916508"],"apc_list":null,"apc_paid":null,"fwci":4.6751,"has_fulltext":true,"cited_by_count":96,"citation_normalized_percentile":{"value":0.94578809,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"7","issue":"1","first_page":null,"last_page":null},"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9800000190734863,"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":0.9577999711036682,"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":0.8107136487960815},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.7663780450820923},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5838923454284668},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5484139323234558},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4872936010360718},{"id":"https://openalex.org/keywords/projective-test","display_name":"Projective test","score":0.4489549398422241},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23851177096366882},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10637515783309937}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8107136487960815},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.7663780450820923},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5838923454284668},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5484139323234558},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4872936010360718},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.4489549398422241},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23851177096366882},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10637515783309937},{"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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1489","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1489","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r11/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.87.156","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.87.156","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_7/PDF/v7i1r11.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1489","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1489","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r11/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1590335557.pdf","grobid_xml":"https://content.openalex.org/works/W1590335557.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W3813004","https://openalex.org/W22700839","https://openalex.org/W72687480","https://openalex.org/W949515176","https://openalex.org/W1194192780","https://openalex.org/W1221443615","https://openalex.org/W1503316974","https://openalex.org/W1519252437","https://openalex.org/W1542754334","https://openalex.org/W1551018093","https://openalex.org/W1565547311","https://openalex.org/W1590335557","https://openalex.org/W1606480398","https://openalex.org/W1973174922","https://openalex.org/W1993894653","https://openalex.org/W2009024256","https://openalex.org/W2018360032","https://openalex.org/W2020224659","https://openalex.org/W2022786957","https://openalex.org/W2039660064","https://openalex.org/W2060414828","https://openalex.org/W2062260188","https://openalex.org/W2062692517","https://openalex.org/W2071138246","https://openalex.org/W2078430577","https://openalex.org/W2105987353","https://openalex.org/W2108680187","https://openalex.org/W2126793274","https://openalex.org/W2134984950","https://openalex.org/W2142035596","https://openalex.org/W2168674495","https://openalex.org/W2171843169","https://openalex.org/W2172400893","https://openalex.org/W2329438091","https://openalex.org/W2481986369","https://openalex.org/W2504591654","https://openalex.org/W2601345000","https://openalex.org/W4210390212","https://openalex.org/W4235416165","https://openalex.org/W4285719527","https://openalex.org/W4300694375","https://openalex.org/W4376561431","https://openalex.org/W6600144636","https://openalex.org/W6602950699","https://openalex.org/W6655593548","https://openalex.org/W6675887628","https://openalex.org/W6678615252","https://openalex.org/W6702196235"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W2953584534","https://openalex.org/W2087729549","https://openalex.org/W2160220654","https://openalex.org/W2531853030","https://openalex.org/W2059367453","https://openalex.org/W2964161525","https://openalex.org/W4312620033","https://openalex.org/W2333957621","https://openalex.org/W2053984978"],"abstract_inverted_index":{"The":[0],"aim":[1],"of":[2,10,48,72],"this":[3],"paper":[4],"is":[5],"to":[6,62],"develop":[7],"a":[8,18,22,35,69],"theory":[9],"linear":[11,26,41],"codes":[12,27,42,60,79],"over":[13,28,43,83],"finite":[14],"chain":[15,44,85],"rings":[16,45],"from":[17],"geometric":[19],"viewpoint.":[20],"Generalizing":[21],"well-known":[23],"result":[24],"for":[25],"fields,":[29],"we":[30,74],"prove":[31],"that":[32,57,76],"there":[33],"exists":[34],"one-to-one":[36],"correspondence":[37],"between":[38],"so-called":[39],"fat":[40],"and":[46,65],"multisets":[47,64,73],"points":[49],"in":[50,54],"projective":[51],"Hjelmslev":[52],"geometries,":[53],"the":[55],"sense":[56],"semilinearly":[58],"isomorphic":[59],"correspond":[61],"equivalent":[63],"vice":[66],"versa.":[67],"Using":[68],"selected":[70],"class":[71],"show":[75],"certain":[77],"MacDonald":[78],"are":[80],"linearly":[81],"representable":[82],"nontrivial":[84],"rings.":[86]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}