{"id":"https://openalex.org/W2173874710","doi":"https://doi.org/10.37236/5213","title":"On the Existence of Certain Optimal Self-Dual Codes with Lengths Between 74 and 116","display_name":"On the Existence of Certain Optimal Self-Dual Codes with Lengths Between 74 and 116","publication_year":2015,"publication_date":"2015-11-27","ids":{"openalex":"https://openalex.org/W2173874710","doi":"https://doi.org/10.37236/5213","mag":"2173874710"},"language":"en","primary_location":{"id":"doi:10.37236/5213","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5213","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p33/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p33/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100375868","display_name":"Tao Zhang","orcid":"https://orcid.org/0000-0002-9914-0382"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Tao Zhang","raw_affiliation_strings":["Zhejiang University"],"affiliations":[{"raw_affiliation_string":"Zhejiang University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066782806","display_name":"Jerod Michel","orcid":"https://orcid.org/0000-0002-7043-6163"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jerod Michel","raw_affiliation_strings":["Zhejiang University"],"affiliations":[{"raw_affiliation_string":"Zhejiang University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049623145","display_name":"Tao Feng","orcid":"https://orcid.org/0000-0002-3276-6129"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao Feng","raw_affiliation_strings":["Zhejiang University"],"affiliations":[{"raw_affiliation_string":"Zhejiang University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029449317","display_name":"Gennian Ge","orcid":"https://orcid.org/0000-0002-1535-0754"},"institutions":[{"id":"https://openalex.org/I96852419","display_name":"Capital Normal University","ror":"https://ror.org/005edt527","country_code":"CN","type":"education","lineage":["https://openalex.org/I96852419"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gennian Ge","raw_affiliation_strings":["Capital Normal University"],"affiliations":[{"raw_affiliation_string":"Capital Normal University","institution_ids":["https://openalex.org/I96852419"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100375868"],"corresponding_institution_ids":["https://openalex.org/I76130692"],"apc_list":null,"apc_paid":null,"fwci":0.4451,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.77347151,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"22","issue":"4","first_page":null,"last_page":null},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9936000108718872,"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":0.9889000058174133,"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/mathematics","display_name":"Mathematics","score":0.8212193250656128},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.7530348896980286},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7041440010070801},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5672295093536377},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5188480615615845},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4593546390533447},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.44023188948631287},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1286163032054901}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8212193250656128},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.7530348896980286},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7041440010070801},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5672295093536377},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5188480615615845},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4593546390533447},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.44023188948631287},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1286163032054901},{"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:10.37236/5213","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5213","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p33/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.747.6113","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.747.6113","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1405.7538.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/5213","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5213","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p33/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1391304095","display_name":null,"funder_award_id":"61571310","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2376276132","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G3214160367","display_name":null,"funder_award_id":"No. 11","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3549223800","display_name":null,"funder_award_id":"61171198","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4020255992","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5167091242","display_name":null,"funder_award_id":"No. 1","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5807587223","display_name":null,"funder_award_id":"11201418","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6057721769","display_name":null,"funder_award_id":"11422112","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7608752429","display_name":null,"funder_award_id":"Talent","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7726157001","display_name":null,"funder_award_id":"Grant No.","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8454121759","display_name":null,"funder_award_id":"11431003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8951484681","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2173874710.pdf","grobid_xml":"https://content.openalex.org/works/W2173874710.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W1496348523","https://openalex.org/W1556398817","https://openalex.org/W1559343931","https://openalex.org/W1617868970","https://openalex.org/W1671456867","https://openalex.org/W1898703922","https://openalex.org/W1963661276","https://openalex.org/W1966360582","https://openalex.org/W1966845969","https://openalex.org/W1967975978","https://openalex.org/W1971037389","https://openalex.org/W1976677460","https://openalex.org/W1979177096","https://openalex.org/W1986692294","https://openalex.org/W1994601465","https://openalex.org/W1994845342","https://openalex.org/W2002390500","https://openalex.org/W2002653308","https://openalex.org/W2006075491","https://openalex.org/W2018939046","https://openalex.org/W2028638311","https://openalex.org/W2032043592","https://openalex.org/W2041664419","https://openalex.org/W2047560238","https://openalex.org/W2050209063","https://openalex.org/W2051164689","https://openalex.org/W2053005988","https://openalex.org/W2060023177","https://openalex.org/W2060988076","https://openalex.org/W2061721328","https://openalex.org/W2067695051","https://openalex.org/W2077721309","https://openalex.org/W2078149511","https://openalex.org/W2114972298","https://openalex.org/W2124107181","https://openalex.org/W2124980282","https://openalex.org/W2146774761","https://openalex.org/W2152592660","https://openalex.org/W2158323177","https://openalex.org/W2164888763","https://openalex.org/W2951113975","https://openalex.org/W2964243057","https://openalex.org/W3101346953","https://openalex.org/W4206775542","https://openalex.org/W4213257702","https://openalex.org/W6644268970","https://openalex.org/W6647014772","https://openalex.org/W6681771338","https://openalex.org/W6683670794"],"related_works":["https://openalex.org/W2317351040","https://openalex.org/W4285447065","https://openalex.org/W1988622314","https://openalex.org/W2393949104","https://openalex.org/W3046201198","https://openalex.org/W4293061921","https://openalex.org/W2952466936","https://openalex.org/W2807441102","https://openalex.org/W4287830728","https://openalex.org/W2372693287"],"abstract_inverted_index":{"The":[0],"existence":[1],"of":[2,22,59,79,95,110],"optimal":[3],"binary":[4,23],"self-dual":[5,24,44,55,75,98,111],"codes":[6,25,45,112],"is":[7,34],"a":[8,27,35],"long-standing":[9],"research":[10],"problem.":[11],"In":[12],"this":[13],"paper,":[14],"we":[15,87],"present":[16],"some":[17,89,106],"results":[18,38],"concerning":[19],"the":[20,92],"decomposition":[21],"with":[26,46,113],"dihedral":[28],"automorphism":[29],"group":[30],"$D_{2p}$,":[31],"where":[32],"$p$":[33],"prime.":[36],"These":[37],"are":[39,70,81],"applied":[40],"to":[41,84,104],"construct":[42],"new":[43,62,82],"length":[47],"$78$":[48],"or":[49],"$116$.":[50],"We":[51,65,100],"obtain":[52],"$16$":[53],"inequivalent":[54,74],"$[78,39,14]$":[56],"codes,":[57,77],"four":[58],"which":[60,80],"have":[61],"weight":[63,93,108],"enumerators.":[64],"also":[66],"show":[67],"that":[68],"there":[69],"at":[71],"least":[72],"$141$":[73],"$[116,58,18]$":[76],"most":[78],"up":[83],"equivalence.":[85],"Meanwhile,":[86],"give":[88],"restrictions":[90,103],"on":[91],"enumerators":[94,109],"singly":[96],"even":[97],"codes.":[99],"use":[101],"these":[102],"exclude":[105],"possible":[107],"lengths":[114],"$74$,":[115],"$76$,":[116],"$82$,":[117],"$98$":[118],"and":[119],"$100$.":[120]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}
