{"id":"https://openalex.org/W3085293166","doi":"https://doi.org/10.3934/amc.2020111","title":"New self-dual codes of length 68 from a $ 2 \\times 2 $ block matrix construction and group rings","display_name":"New self-dual codes of length 68 from a $ 2 \\times 2 $ block matrix construction and group rings","publication_year":2020,"publication_date":"2020-09-18","ids":{"openalex":"https://openalex.org/W3085293166","doi":"https://doi.org/10.3934/amc.2020111","mag":"3085293166"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2020111","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2020111","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/amc.2020111","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058113491","display_name":"Maria Bortos","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Maria Bortos","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074733092","display_name":"Joe Gildea","orcid":"https://orcid.org/0000-0001-7242-779X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Joe Gildea","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070013407","display_name":"Abidin Kaya","orcid":"https://orcid.org/0000-0003-0175-1909"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abidin Kaya","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042655752","display_name":"Adrian Korban","orcid":"https://orcid.org/0000-0001-5206-6480"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Adrian Korban","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5022194058","display_name":"Alexander Tylyshchak","orcid":"https://orcid.org/0000-0001-7828-3416"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexander Tylyshchak","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5058113491"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6858,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.76885321,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"16","issue":"2","first_page":"269","last_page":"269"},"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":0.9932000041007996,"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":0.9768999814987183,"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":0.786358118057251},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5689376592636108},{"id":"https://openalex.org/keywords/generator-matrix","display_name":"Generator matrix","score":0.5090529322624207},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.47645190358161926},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4740409851074219},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4272051155567169},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13989847898483276},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1121971607208252}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.786358118057251},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5689376592636108},{"id":"https://openalex.org/C1842014","wikidata":"https://www.wikidata.org/wiki/Q1502046","display_name":"Generator matrix","level":3,"score":0.5090529322624207},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.47645190358161926},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4740409851074219},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4272051155567169},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13989847898483276},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1121971607208252},{"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/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"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},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2020111","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2020111","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2020111","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2020111","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.46000000834465027}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1967975978","https://openalex.org/W1969278167","https://openalex.org/W1976677460","https://openalex.org/W1982193070","https://openalex.org/W2006075491","https://openalex.org/W2054795976","https://openalex.org/W2061721328","https://openalex.org/W2093455304","https://openalex.org/W2114972298","https://openalex.org/W2135814280","https://openalex.org/W2168041697","https://openalex.org/W2398687428","https://openalex.org/W2608538340","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/W3015351830","https://openalex.org/W3046379320","https://openalex.org/W3047057787","https://openalex.org/W3097352577","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W2122698785","https://openalex.org/W2345600497","https://openalex.org/W241866648","https://openalex.org/W305319458","https://openalex.org/W3198007960","https://openalex.org/W2047454787","https://openalex.org/W3098318101","https://openalex.org/W2604978577","https://openalex.org/W2597330968"],"abstract_inverted_index":{"<p":[0],"style='text-indent:20px;'>Many":[1],"generator":[2,67],"matrices":[3],"for":[4,119],"constructing":[5],"extremal":[6,127],"binary":[7,128,152,188],"self-dual":[8,129,153,189],"codes":[9,130,143],"of":[10,131],"different":[11],"lengths":[12],"have":[13],"the":[14,32,47,58,80,97,101,116,142,161],"form":[15],"<inline-formula><tex-math":[16,27,33,42,48,71,88,109,154,164,172,177,190],"id=\"M1\">\\begin{document}$":[17],"G":[18],"=":[19,167],"(I_n":[20],"\\":[21,23],"|":[22],"A),":[24],"$\\end{document}</tex-math></inline-formula>":[25,30,38,45,53,74,91,112,170,175,181],"where":[26,79],"id=\"M2\">\\begin{document}$":[28],"I_n":[29],"is":[31,46,75,92],"id=\"M3\">\\begin{document}$":[34],"n":[35,37,50,52],"\\times":[36,51],"identity":[39],"matrix":[40,54,68],"and":[41,86,113,171],"id=\"M4\">\\begin{document}$":[43],"A":[44,73,90],"id=\"M5\">\\begin{document}$":[49],"fully":[55,94],"determined":[56,95],"by":[57,96,114,135],"first":[59,102],"row.":[60,103],"In":[61,182],"this":[62],"work,":[63],"we":[64,121,145,184],"define":[65],"a":[66,76,137],"in":[69,100,176],"which":[70],"id=\"M6\">\\begin{document}$":[72],"block":[77],"matrix,":[78],"blocks":[81],"come":[82],"from":[83],"group":[84],"rings":[85],"also,":[87],"id=\"M7\">\\begin{document}$":[89],"not":[93],"elements":[98],"appearing":[99],"By":[104],"applying":[105],"our":[106],"construction":[107],"over":[108],"id=\"M8\">\\begin{document}$":[110],"\\mathbb{F}_2+u\\mathbb{F}_2":[111],"employing":[115,136],"extension":[117],"method":[118,140],"codes,":[120],"were":[122,146],"able":[123,147],"to":[124,141,148],"construct":[125,149],"new":[126,151,187],"length":[132],"68.":[133],"Additionally,":[134],"generalised":[138],"neighbour":[139],"obtained,":[144],"many":[150],"id=\"M9\">\\begin{document}$":[155],"[68,":[156,192],"34,":[157,193],"12]":[158,194],"$\\end{document}</tex-math></inline-formula>-codes":[159],"with":[160],"rare":[162],"parameters":[163],"id=\"M10\">\\begin{document}$":[165],"\\gamma":[166],"7,":[168],"8":[169],"id=\"M11\">\\begin{document}$":[173],"9":[174],"id=\"M12\">\\begin{document}$":[178],"W_{68,":[179],"2}.":[180],"particular,":[183],"find":[185],"92":[186],"id=\"M13\">\\begin{document}$":[191],"$\\end{document}</tex-math></inline-formula>-codes.</p>":[195]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}