{"id":"https://openalex.org/W3007939378","doi":"https://doi.org/10.1007/s10623-021-00882-8","title":"Composite matrices from group rings, composite G-codes and constructions of self-dual codes","display_name":"Composite matrices from group rings, composite G-codes and constructions of self-dual codes","publication_year":2021,"publication_date":"2021-05-19","ids":{"openalex":"https://openalex.org/W3007939378","doi":"https://doi.org/10.1007/s10623-021-00882-8","mag":"3007939378"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-021-00882-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-021-00882-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-021-00882-8.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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","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/s10623-021-00882-8.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":"Steven T. Dougherty","raw_affiliation_strings":["Department of Mathematics, University of Scranton, Scranton, PA 18510, USA","Department of Mathematics, University of Scranton, Scranton, USA"],"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, USA","institution_ids":["https://openalex.org/I124113063"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074733092","display_name":"Joe Gildea","orcid":"https://orcid.org/0000-0001-7242-779X"},"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":"Joe Gildea","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/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":"last","author":{"id":"https://openalex.org/A5070013407","display_name":"Abidin Kaya","orcid":"https://orcid.org/0000-0003-0175-1909"},"institutions":[{"id":"https://openalex.org/I1302752606","display_name":"Houston Advanced Research Center","ror":"https://ror.org/0413xn342","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1302752606"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Abidin Kaya","raw_affiliation_strings":["Harmony School of Technology, Houston TX 77038, USA","Harmony School of Technology, Houston, USA"],"affiliations":[{"raw_affiliation_string":"Harmony School of Technology, Houston TX 77038, USA","institution_ids":["https://openalex.org/I1302752606"]},{"raw_affiliation_string":"Harmony School of Technology, Houston, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"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":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00489999,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"89","issue":"7","first_page":"1615","last_page":"1638"},"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/T10849","display_name":"Finite Group Theory Research","score":0.9973999857902527,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9915000200271606,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/group-ring","display_name":"Group ring","score":0.6790022253990173},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.6088352799415588},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5973610877990723},{"id":"https://openalex.org/keywords/generator-matrix","display_name":"Generator matrix","score":0.5943999886512756},{"id":"https://openalex.org/keywords/composite-number","display_name":"Composite number","score":0.5943328142166138},{"id":"https://openalex.org/keywords/group-code","display_name":"Group code","score":0.5925813913345337},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.5754752159118652},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4908314645290375},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.4884404242038727},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48594343662261963},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.46458321809768677},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.4476288855075836},{"id":"https://openalex.org/keywords/finite-group","display_name":"Finite group","score":0.4247055649757385},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.4172722101211548},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4167400896549225},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.3549080491065979},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.248200923204422},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16245335340499878},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10989344120025635},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.0684594213962555}],"concepts":[{"id":"https://openalex.org/C76572486","wikidata":"https://www.wikidata.org/wiki/Q2602722","display_name":"Group ring","level":3,"score":0.6790022253990173},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6088352799415588},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5973610877990723},{"id":"https://openalex.org/C1842014","wikidata":"https://www.wikidata.org/wiki/Q1502046","display_name":"Generator matrix","level":3,"score":0.5943999886512756},{"id":"https://openalex.org/C104779481","wikidata":"https://www.wikidata.org/wiki/Q50707","display_name":"Composite number","level":2,"score":0.5943328142166138},{"id":"https://openalex.org/C3427991","wikidata":"https://www.wikidata.org/wiki/Q651426","display_name":"Group code","level":5,"score":0.5925813913345337},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5754752159118652},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4908314645290375},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.4884404242038727},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48594343662261963},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.46458321809768677},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.4476288855075836},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.4247055649757385},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.4172722101211548},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4167400896549225},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.3549080491065979},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.248200923204422},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16245335340499878},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10989344120025635},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0684594213962555},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10623-021-00882-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-021-00882-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-021-00882-8.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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2002.11614","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.11614","pdf_url":"https://arxiv.org/pdf/2002.11614","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":null,"raw_type":"text"},{"id":"mag:3007939378","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2002.11614v1","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.2002.11614","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2002.11614","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/s10623-021-00882-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-021-00882-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-021-00882-8.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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3007939378.pdf","grobid_xml":"https://content.openalex.org/works/W3007939378.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1508421660","https://openalex.org/W1976677460","https://openalex.org/W2006075491","https://openalex.org/W2051648459","https://openalex.org/W2054795976","https://openalex.org/W2061721328","https://openalex.org/W2067264852","https://openalex.org/W2071993485","https://openalex.org/W2093455304","https://openalex.org/W2135814280","https://openalex.org/W2168041697","https://openalex.org/W2184289418","https://openalex.org/W2344135815","https://openalex.org/W2608538340","https://openalex.org/W2732873618","https://openalex.org/W2767540775","https://openalex.org/W2784777098","https://openalex.org/W2789708407","https://openalex.org/W2915747783","https://openalex.org/W2953411685","https://openalex.org/W2988740442","https://openalex.org/W2989936149","https://openalex.org/W2995870774","https://openalex.org/W3015351830","https://openalex.org/W3046379320","https://openalex.org/W3047057787","https://openalex.org/W3134775645","https://openalex.org/W3151406557"],"related_works":["https://openalex.org/W3161039860","https://openalex.org/W3127192053","https://openalex.org/W2767540775","https://openalex.org/W3128298405","https://openalex.org/W3047057787","https://openalex.org/W3177094578","https://openalex.org/W3015351830","https://openalex.org/W3097636042","https://openalex.org/W2784777098","https://openalex.org/W2345012195","https://openalex.org/W3097352577","https://openalex.org/W1996717410","https://openalex.org/W2135472283","https://openalex.org/W3016550227","https://openalex.org/W1975802161","https://openalex.org/W1617825208","https://openalex.org/W3169999406","https://openalex.org/W3006398879","https://openalex.org/W3003401666","https://openalex.org/W2314704409"],"abstract_inverted_index":{"Abstract":[0],"In":[1,136],"this":[2],"work,":[3],"we":[4,75,105,138,145,150],"define":[5,70],"composite":[6,22,59,65,87],"matrices":[7,84],"which":[8,79],"are":[9,30,152],"derived":[10],"from":[11,154],"group":[12,34],"rings.":[13],"We":[14,25,52,68],"extend":[15],"the":[16,37,55,82,86,91,94,99,119,148],"idea":[17],"of":[18,57,81,111],"G":[19,23,46,60,66,72],"-codes":[20],"to":[21],"-codes.":[24,73],"show":[26,146],"that":[27,54,147],"these":[28],"codes":[29,110,149],"ideals":[31],"in":[32],"a":[33,40,58,64],"ring,":[35],"where":[36],"ring":[38,44],"is":[39,47,62],"finite":[41,50],"commutative":[42],"Frobenius":[43],"and":[45,85,102,134],"an":[48],"arbitrary":[49],"group.":[51],"prove":[53],"dual":[56],"-code":[61],"also":[63,69],"-code.":[67],"quasi-composite":[71],"Additionally,":[74],"study":[76],"generator":[77,92],"matrices,":[78,93],"consist":[80],"identity":[83],"matrices.":[88],"Together":[89],"with":[90,114],"well":[95],"known":[96],"extension":[97],"method,":[98],"neighbour":[100],"method":[101],"its":[103],"generalization,":[104],"find":[106,139,151],"extremal":[107],"binary":[108],"self-dual":[109],"length":[112],"68":[113],"new":[115,141],"weight":[116],"enumerators":[117],"for":[118],"rare":[120],"parameters":[121],"$$\\gamma":[122],"=7,8$$":[123],"<mml:math":[124],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[125],"<mml:mrow>":[126],"<mml:mi>\u03b3</mml:mi>":[127],"<mml:mo>=</mml:mo>":[128],"<mml:mn>7</mml:mn>":[129],"<mml:mo>,</mml:mo>":[130],"<mml:mn>8</mml:mn>":[131],"</mml:mrow>":[132],"</mml:math>":[133],"9.":[135],"particular,":[137],"49":[140],"such":[142],"codes.":[143],"Moreover,":[144],"inaccessible":[153],"other":[155],"construction":[156]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}