{"id":"https://openalex.org/W3128298405","doi":"https://doi.org/10.1007/s00200-021-00504-9","title":"Group matrix ring codes and constructions of self-dual codes","display_name":"Group matrix ring codes and constructions of self-dual codes","publication_year":2021,"publication_date":"2021-04-02","ids":{"openalex":"https://openalex.org/W3128298405","doi":"https://doi.org/10.1007/s00200-021-00504-9","mag":"3128298405"},"language":"en","primary_location":{"id":"doi:10.1007/s00200-021-00504-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00200-021-00504-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00200-021-00504-9.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00200-021-00504-9.pdf","any_repository_has_fulltext":true},"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":"S. T. Dougherty","raw_affiliation_strings":["University of Scranton, Scranton, PA, 18518, USA","University of Scranton, Scranton, USA"],"affiliations":[{"raw_affiliation_string":"University of Scranton, Scranton, PA, 18518, USA","institution_ids":["https://openalex.org/I124113063"]},{"raw_affiliation_string":"University of Scranton, Scranton, USA","institution_ids":["https://openalex.org/I124113063"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042655752","display_name":"Adrian Korban","orcid":"https://orcid.org/0000-0001-5206-6480"},"institutions":[{"id":"https://openalex.org/I137265193","display_name":"University of Chester","ror":"https://ror.org/01drpwb22","country_code":"GB","type":"education","lineage":["https://openalex.org/I137265193"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Adrian Korban","raw_affiliation_strings":["Department of Mathematical and Physical Sciences, University of Chester, Thornton Science Park, Pool Ln, Chester, CH2 4NU, England","Department of Mathematical and Physical Sciences, University of Chester, Chester, England"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical and Physical Sciences, University of Chester, Thornton Science Park, Pool Ln, Chester, CH2 4NU, England","institution_ids":["https://openalex.org/I137265193"]},{"raw_affiliation_string":"Department of Mathematical and Physical Sciences, University of Chester, Chester, England","institution_ids":["https://openalex.org/I137265193"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068178531","display_name":"Serap \u015eahinkaya","orcid":"https://orcid.org/0000-0002-2084-6260"},"institutions":[{"id":"https://openalex.org/I4210132115","display_name":"Tarsus University","ror":"https://ror.org/0397szj42","country_code":"TR","type":"education","lineage":["https://openalex.org/I4210132115"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Serap \u015eahinkaya","raw_affiliation_strings":["Faculty of Engineering Department of Natural and Mathematical Sciences, Tarsus University, Mersin, Turkey"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering Department of Natural and Mathematical Sciences, Tarsus University, Mersin, Turkey","institution_ids":["https://openalex.org/I4210132115"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023224914","display_name":"Deniz \u00dcst\u00fcn","orcid":"https://orcid.org/0000-0002-5229-4018"},"institutions":[{"id":"https://openalex.org/I4210132115","display_name":"Tarsus University","ror":"https://ror.org/0397szj42","country_code":"TR","type":"education","lineage":["https://openalex.org/I4210132115"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Deniz Ustun","raw_affiliation_strings":["Faculty of Engineering Department of Computer Engineering, Tarsus University, Mersin, Turkey"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering Department of Computer Engineering, Tarsus University, Mersin, Turkey","institution_ids":["https://openalex.org/I4210132115"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5059969175"],"corresponding_institution_ids":["https://openalex.org/I124113063"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.1397,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51672506,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"34","issue":"2","first_page":"279","last_page":"299"},"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/T10849","display_name":"Finite Group Theory Research","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9962999820709229,"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/generator-matrix","display_name":"Generator matrix","score":0.7905811667442322},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.6548688411712646},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5972436666488647},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5355671644210815},{"id":"https://openalex.org/keywords/group-ring","display_name":"Group ring","score":0.5333830118179321},{"id":"https://openalex.org/keywords/group-code","display_name":"Group code","score":0.531211256980896},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.48842233419418335},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47029611468315125},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.44379839301109314},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4276198744773865},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.42350322008132935},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.39775633811950684},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.3811469078063965},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.3545670509338379},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.22880542278289795},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19926601648330688},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1531323790550232},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.0814346969127655},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.08023977279663086}],"concepts":[{"id":"https://openalex.org/C1842014","wikidata":"https://www.wikidata.org/wiki/Q1502046","display_name":"Generator matrix","level":3,"score":0.7905811667442322},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.6548688411712646},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5972436666488647},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5355671644210815},{"id":"https://openalex.org/C76572486","wikidata":"https://www.wikidata.org/wiki/Q2602722","display_name":"Group ring","level":3,"score":0.5333830118179321},{"id":"https://openalex.org/C3427991","wikidata":"https://www.wikidata.org/wiki/Q651426","display_name":"Group code","level":5,"score":0.531211256980896},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.48842233419418335},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47029611468315125},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.44379839301109314},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4276198744773865},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.42350322008132935},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.39775633811950684},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.3811469078063965},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3545670509338379},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.22880542278289795},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19926601648330688},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1531323790550232},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0814346969127655},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.08023977279663086},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00200-021-00504-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00200-021-00504-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00200-021-00504-9.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2102.00475","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2102.00475","pdf_url":"https://arxiv.org/pdf/2102.00475","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:3128298405","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2102.00475.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2102.00475","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2102.00475","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s00200-021-00504-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00200-021-00504-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00200-021-00504-9.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.6700000166893005}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3128298405.pdf","grobid_xml":"https://content.openalex.org/works/W3128298405.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W789681013","https://openalex.org/W1976677460","https://openalex.org/W2090783432","https://openalex.org/W2114972298","https://openalex.org/W2135814280","https://openalex.org/W2158323177","https://openalex.org/W2166623707","https://openalex.org/W2262428787","https://openalex.org/W2272944842","https://openalex.org/W2732873618","https://openalex.org/W2767540775","https://openalex.org/W2963858752","https://openalex.org/W3098154057"],"related_works":["https://openalex.org/W3140465573","https://openalex.org/W2767540775","https://openalex.org/W2963858752","https://openalex.org/W3007939378","https://openalex.org/W3127192053","https://openalex.org/W3003487651","https://openalex.org/W1595335682","https://openalex.org/W1787518919","https://openalex.org/W1617825208","https://openalex.org/W2177092276","https://openalex.org/W2314704409","https://openalex.org/W2105987353","https://openalex.org/W2998153734","https://openalex.org/W2038702067","https://openalex.org/W1501126651","https://openalex.org/W2784777098","https://openalex.org/W3015351830","https://openalex.org/W2029706920","https://openalex.org/W2037659346","https://openalex.org/W2090256001"],"abstract_inverted_index":{"Abstract":[0],"In":[1,174],"this":[2,150,172],"work,":[3],"we":[4,22,132,176],"study":[5],"codes":[6,26,65,112,158,170],"generated":[7],"by":[8],"elements":[9],"that":[10,64],"come":[11],"from":[12],"group":[13,90],"matrix":[14,19,33,91,136,146,152],"rings.":[15],"We":[16,62,148],"present":[17],"a":[18,134],"construction":[20],"which":[21,140],"use":[23],"to":[24,153],"generate":[25],"in":[27,88],"two":[28],"different":[29],"ambient":[30],"spaces:":[31],"the":[32,51,58,67,89,110,114,143],"ring":[34,52,68,92,115],"$$M_k(R)$$":[35,69],"<mml:math":[36,70,94,119],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[37,71,95,120],"<mml:mrow>":[38,43,72,77,96,101],"<mml:msub>":[39,73,97],"<mml:mi>M</mml:mi>":[40,74,98],"<mml:mi>k</mml:mi>":[41,75,99,123],"</mml:msub>":[42,76,100],"<mml:mo>(</mml:mo>":[44,78,102],"<mml:mi>R</mml:mi>":[45,79,103],"<mml:mo>)</mml:mo>":[46,80,104],"</mml:mrow>":[47,48,81,82,105,107],"</mml:math>":[49,83,108,125],"and":[50,109,164,168,182],"R":[53,56,116],",":[54],"where":[55],"is":[57],"commutative":[59],"Frobenius":[60],"ring.":[61],"show":[63],"over":[66,113],"are":[84,117],"one":[85],"sided":[86],"ideals":[87],"$$M_k(R)G$$":[93],"<mml:mi>G</mml:mi>":[106,122],"corresponding":[111],"$$G^k$$":[118],"<mml:msup>":[121],"</mml:msup>":[124],"-codes":[126],"of":[127,142,171],"length":[128],"kn":[129],".":[130],"Additionally,":[131],"give":[133],"generator":[135,151],"for":[137,155],"self-dual":[138,157,191],"codes,":[139],"consist":[141],"mentioned":[144],"above":[145],"construction.":[147],"employ":[149],"search":[154],"binary":[156,187],"with":[159],"parameters":[160],"[72,":[161,188],"36,":[162,189],"12]":[163,190],"find":[165],"new":[166,179,184],"singly-even":[167],"doubly-even":[169],"type.":[173],"particular,":[175],"construct":[177],"16":[178],"Type":[180,185],"I":[181],"4":[183],"II":[186],"codes.":[192]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}