{"id":"https://openalex.org/W3198901854","doi":"https://doi.org/10.3934/amc.2022021","title":"Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours","display_name":"Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours","publication_year":2022,"publication_date":"2022-04-02","ids":{"openalex":"https://openalex.org/W3198901854","doi":"https://doi.org/10.3934/amc.2022021","mag":"3198901854"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2022021","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2022021","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/amc.2022021","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074733092","display_name":"Joe Gildea","orcid":"https://orcid.org/0000-0001-7242-779X"},"institutions":[{"id":"https://openalex.org/I94876832","display_name":"Dundalk Institute of Technology","ror":"https://ror.org/01800zd49","country_code":"IE","type":"education","lineage":["https://openalex.org/I94876832"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Joe Gildea","raw_affiliation_strings":["Department of Computing Science and Mathematics, School of Informatics and Creative Arts, Dundalk Institute of Technology, Dundalk, County Louth, A91 K584, Ireland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing Science and Mathematics, School of Informatics and Creative Arts, Dundalk Institute of Technology, Dundalk, County Louth, A91 K584, Ireland","institution_ids":["https://openalex.org/I94876832"]}]},{"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 Physical, Mathematical and Engineering Sciences, University of Chester, Exton Park, Chester, CH1 4AR, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physical, Mathematical and Engineering Sciences, University of Chester, Exton Park, Chester, CH1 4AR, United Kingdom","institution_ids":["https://openalex.org/I137265193"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066365359","display_name":"Adam Michael Roberts","orcid":"https://orcid.org/0000-0002-0654-7096"},"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":true,"raw_author_name":"Adam M. Roberts","raw_affiliation_strings":["Department of Physical, Mathematical and Engineering Sciences, University of Chester, Exton Park, Chester, CH1 4AR, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physical, Mathematical and Engineering Sciences, University of Chester, Exton Park, Chester, CH1 4AR, United Kingdom","institution_ids":["https://openalex.org/I137265193"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022194058","display_name":"Alexander Tylyshchak","orcid":"https://orcid.org/0000-0001-7828-3416"},"institutions":[{"id":"https://openalex.org/I4210149306","display_name":"Ferenc Rakoczi II Transcarpathian Hungarian University","ror":"https://ror.org/042q4h794","country_code":"UA","type":"education","lineage":["https://openalex.org/I4210149306"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Alexander Tylyshchak","raw_affiliation_strings":["Ferenc R\u00e1k\u00f3czi II Transcarpathian Hungarian College of Higher Education, Berehove, Zakarpattia Oblast, 90201, Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ferenc R\u00e1k\u00f3czi II Transcarpathian Hungarian College of Higher Education, Berehove, Zakarpattia Oblast, 90201, Ukraine","institution_ids":["https://openalex.org/I4210149306"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066365359"],"corresponding_institution_ids":["https://openalex.org/I137265193"],"apc_list":null,"apc_paid":null,"fwci":0.4585,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.66350203,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"18","issue":"3","first_page":"738","last_page":"752"},"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":0.9937000274658203,"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":0.9732999801635742,"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":0.8575984239578247},{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.6703680753707886},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5730587840080261},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.5591318607330322},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5371096730232239},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5335403680801392},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44430315494537354},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.4269358515739441},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.4141859710216522},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.23430365324020386},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.056365370750427246}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8575984239578247},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.6703680753707886},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5730587840080261},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5591318607330322},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5371096730232239},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5335403680801392},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44430315494537354},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.4269358515739441},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.4141859710216522},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.23430365324020386},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.056365370750427246},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"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/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/amc.2022021","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2022021","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"},{"id":"pmh:oai:arXiv.org:2109.00908","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2109.00908","pdf_url":"https://arxiv.org/pdf/2109.00908","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"}],"best_oa_location":{"id":"doi:10.3934/amc.2022021","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2022021","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":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.6100000143051147}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":62,"referenced_works":["https://openalex.org/W143087697","https://openalex.org/W832720774","https://openalex.org/W1556398817","https://openalex.org/W1969278167","https://openalex.org/W1973620888","https://openalex.org/W1976677460","https://openalex.org/W1994268719","https://openalex.org/W1997244490","https://openalex.org/W2014468280","https://openalex.org/W2054795976","https://openalex.org/W2055821713","https://openalex.org/W2061721328","https://openalex.org/W2070622268","https://openalex.org/W2078149511","https://openalex.org/W2114972298","https://openalex.org/W2124980282","https://openalex.org/W2130978598","https://openalex.org/W2135814280","https://openalex.org/W2142858721","https://openalex.org/W2143423882","https://openalex.org/W2152592660","https://openalex.org/W2158323177","https://openalex.org/W2168041697","https://openalex.org/W2168761207","https://openalex.org/W2169607896","https://openalex.org/W2183688201","https://openalex.org/W2262428787","https://openalex.org/W2273707724","https://openalex.org/W2398687428","https://openalex.org/W2623374973","https://openalex.org/W2684240765","https://openalex.org/W2732873618","https://openalex.org/W2753520862","https://openalex.org/W2784777098","https://openalex.org/W2789708407","https://openalex.org/W2915747783","https://openalex.org/W2953411685","https://openalex.org/W2963382198","https://openalex.org/W2964083059","https://openalex.org/W2966853671","https://openalex.org/W2969305314","https://openalex.org/W2969909077","https://openalex.org/W2988740442","https://openalex.org/W2989936149","https://openalex.org/W2998358951","https://openalex.org/W2999726184","https://openalex.org/W3006398879","https://openalex.org/W3015351830","https://openalex.org/W3020986183","https://openalex.org/W3046379320","https://openalex.org/W3047057787","https://openalex.org/W3049148467","https://openalex.org/W3085293166","https://openalex.org/W3097352577","https://openalex.org/W3098154057","https://openalex.org/W3107417051","https://openalex.org/W3124150840","https://openalex.org/W3125597906","https://openalex.org/W3129433258","https://openalex.org/W3161039860","https://openalex.org/W3193472399","https://openalex.org/W3195929678"],"related_works":["https://openalex.org/W2293441232","https://openalex.org/W2964083059","https://openalex.org/W4308298797","https://openalex.org/W2360590989","https://openalex.org/W4255963200","https://openalex.org/W4255391830","https://openalex.org/W2369074270","https://openalex.org/W2408222820","https://openalex.org/W2253391970","https://openalex.org/W2953844587"],"abstract_inverted_index":{"<p":[0],"style='text-indent:20px;'>In":[1],"this":[2],"work,":[3],"we":[4,51],"define":[5],"a":[6,9],"modification":[7],"of":[8,39,57],"bordered":[10],"construction":[11,29,45],"for":[12,27],"self-dual":[13,32,55],"codes":[14,33,56],"which":[15],"utilises":[16],"<inline-formula><tex-math":[17],"id=\"M1\">\\begin{document}$":[18],"\\lambda":[19],"$\\end{document}</tex-math></inline-formula>-circulant":[20],"matrices.":[21],"We":[22],"provide":[23],"the":[24,28,43,48],"necessary":[25],"conditions":[26],"to":[30,73],"produce":[31],"over":[34],"finite":[35],"commutative":[36],"Frobenius":[37],"rings":[38],"characteristic":[40],"2.":[41],"Using":[42],"modified":[44],"together":[46],"with":[47,64],"neighbour":[49],"construction,":[50],"construct":[52],"many":[53],"binary":[54],"lengths":[58],"54,":[59],"68,":[60],"82":[61],"and":[62],"94":[63],"weight":[65],"enumerators":[66],"that":[67],"have":[68],"previously":[69],"not":[70],"been":[71],"known":[72],"exist.":[74]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2021-09-13T00:00:00"}