{"id":"https://openalex.org/W2166904350","doi":"https://doi.org/10.1109/tit.2005.859291","title":"Optimal Linear Codes From Matrix Groups","display_name":"Optimal Linear Codes From Matrix Groups","publication_year":2005,"publication_date":"2005-11-22","ids":{"openalex":"https://openalex.org/W2166904350","doi":"https://doi.org/10.1109/tit.2005.859291","mag":"2166904350"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2005.859291","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5079433304","display_name":"Michael Braun","orcid":"https://orcid.org/0000-0001-9816-2216"},"institutions":[{"id":"https://openalex.org/I1325886976","display_name":"Siemens (Germany)","ror":"https://ror.org/059mq0909","country_code":"DE","type":"funder","lineage":["https://openalex.org/I1325886976"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M. Braun","raw_affiliation_strings":["Department for IT Security, Siemens AG, Munich, Germany"],"affiliations":[{"raw_affiliation_string":"Department for IT Security, Siemens AG, Munich, Germany","institution_ids":["https://openalex.org/I1325886976"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090151569","display_name":"Axel Kohnert","orcid":null},"institutions":[{"id":"https://openalex.org/I54009628","display_name":"University of Bayreuth","ror":"https://ror.org/0234wmv40","country_code":"DE","type":"education","lineage":["https://openalex.org/I54009628"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"A. Kohnert","raw_affiliation_strings":["Mathematical Department, University of Bayreuth, Munich, Germany"],"affiliations":[{"raw_affiliation_string":"Mathematical Department, University of Bayreuth, Munich, Germany","institution_ids":["https://openalex.org/I54009628"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025685163","display_name":"Alfred Wassermann","orcid":"https://orcid.org/0000-0001-5946-668X"},"institutions":[{"id":"https://openalex.org/I54009628","display_name":"University of Bayreuth","ror":"https://ror.org/0234wmv40","country_code":"DE","type":"education","lineage":["https://openalex.org/I54009628"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"A. Wassermann","raw_affiliation_strings":["Mathematical Department, University of Bayreuth, Munich, Germany"],"affiliations":[{"raw_affiliation_string":"Mathematical Department, University of Bayreuth, Munich, Germany","institution_ids":["https://openalex.org/I54009628"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.408,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":26,"citation_normalized_percentile":{"value":0.904079,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":89},"biblio":{"volume":"51","issue":"12","first_page":"4247","last_page":"4251"},"is_retracted":false,"is_paratext":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":0.9952,"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":0.9894,"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/matrix","display_name":"Matrix (chemical analysis)","score":0.5045756}],"concepts":[{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.7680086},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.73630154},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.65644497},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.6173525},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5045756},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.48044965},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4678059},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.432778},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.33716583},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22545823},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15624702},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.14710721},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2005.859291","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":11,"referenced_works":["https://openalex.org/W1482956368","https://openalex.org/W1504661033","https://openalex.org/W1560680010","https://openalex.org/W1582371590","https://openalex.org/W1602235267","https://openalex.org/W1965097372","https://openalex.org/W2076359942","https://openalex.org/W2084294183","https://openalex.org/W2087677220","https://openalex.org/W2129807965","https://openalex.org/W2229871733"],"related_works":["https://openalex.org/W917159298","https://openalex.org/W832867880","https://openalex.org/W4386066307","https://openalex.org/W2460434904","https://openalex.org/W2151857680","https://openalex.org/W2147254059","https://openalex.org/W2113911300","https://openalex.org/W1975697476","https://openalex.org/W1789159349","https://openalex.org/W135568846"],"abstract_inverted_index":{"New":[0],"linear":[1,26,45],"codes":[2,81],"(sometimes":[3],"optimal)":[4],"over":[5],"the":[6,22,34,51,54,58,83],"finite":[7],"field":[8],"with":[9,28,66],"q":[10],"elements":[11],"are":[12],"constructed.":[13],"In":[14],"order":[15],"to":[16,64,75],"do":[17],"this,":[18],"an":[19],"equivalence":[20],"between":[21],"existence":[23,35],"of":[24,36,39,43,53,56],"a":[25,29,37,40],"code":[27],"prescribed":[30],"minimum":[31],"distance":[32],"and":[33],"solution":[38],"certain":[41],"system":[42,55],"Diophantine":[44],"equations":[46],"is":[47,62],"used.":[48],"To":[49],"reduce":[50],"size":[52],"equations,":[57],"search":[59],"for":[60,82],"solutions":[61,65],"restricted":[63],"special":[67],"symmetry":[68],"given":[69],"by":[70],"matrix":[71],"groups.":[72],"This":[73],"allows":[74],"find":[76],"more":[77],"than":[78],"400":[79],"new":[80],"case":[84],"q=2,3,4,5,7,9.":[85]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2166904350","counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-02-23T20:38:43.555907","created_date":"2016-06-24"}