{"id":"https://openalex.org/W2886830976","doi":"https://doi.org/10.3934/amc.2018036","title":"On self-orthogonal designs and codes related to Held's simple group","display_name":"On self-orthogonal designs and codes related to Held's simple group","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2886830976","doi":"https://doi.org/10.3934/amc.2018036","mag":"2886830976"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2018036","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2018036","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.2018036","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023779796","display_name":"Dean Crnkovi\u0107","orcid":"https://orcid.org/0000-0002-3299-7859"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Crnkovi\u0107 Dean","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107115696","display_name":"Vedrana Mikuli\u0107 Crnkovi\u0107","orcid":"https://orcid.org/0000-0003-0757-0009"},"institutions":[{"id":"https://openalex.org/I154347574","display_name":"University of Rijeka","ror":"https://ror.org/05r8dqr10","country_code":"HR","type":"education","lineage":["https://openalex.org/I154347574"]}],"countries":["HR"],"is_corresponding":false,"raw_author_name":"Vedrana Mikuli\u0107 Crnkovi\u0107","raw_affiliation_strings":["Department of Mathematics, University of Rijeka, Radmile Matej\u010di\u0107 2, 51000 Rijeka, Croatia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Rijeka, Radmile Matej\u010di\u0107 2, 51000 Rijeka, Croatia","institution_ids":["https://openalex.org/I154347574"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050001193","display_name":"B. G. Rodrigues","orcid":"https://orcid.org/0000-0002-1349-0219"},"institutions":[{"id":"https://openalex.org/I95023434","display_name":"University of KwaZulu-Natal","ror":"https://ror.org/04qzfn040","country_code":"ZA","type":"education","lineage":["https://openalex.org/I95023434"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Bernardo G. Rodrigues","raw_affiliation_strings":["School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, University Road Private Bag X54001, Westville Campus, Durban 4041, South Africa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, University Road Private Bag X54001, Westville Campus, Durban 4041, South Africa","institution_ids":["https://openalex.org/I95023434"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1822,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.63678526,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"12","issue":"3","first_page":"607","last_page":"628"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9962000250816345,"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":0.9962000250816345,"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":0.9926999807357788,"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":0.98580002784729,"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":0.9216465950012207},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.7468248009681702},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.6015012264251709},{"id":"https://openalex.org/keywords/simple-group","display_name":"Simple group","score":0.5780569911003113},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5252285003662109},{"id":"https://openalex.org/keywords/orthogonal-array","display_name":"Orthogonal array","score":0.4117138385772705},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.34503263235092163},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3209426999092102},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19662350416183472}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9216465950012207},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.7468248009681702},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6015012264251709},{"id":"https://openalex.org/C5383885","wikidata":"https://www.wikidata.org/wiki/Q571124","display_name":"Simple group","level":3,"score":0.5780569911003113},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5252285003662109},{"id":"https://openalex.org/C42632107","wikidata":"https://www.wikidata.org/wiki/Q2031860","display_name":"Orthogonal array","level":3,"score":0.4117138385772705},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.34503263235092163},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3209426999092102},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19662350416183472},{"id":"https://openalex.org/C83469408","wikidata":"https://www.wikidata.org/wiki/Q2036525","display_name":"Taguchi methods","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2018036","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2018036","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.2018036","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2018036","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1606192870","https://openalex.org/W1976677460","https://openalex.org/W1998514724","https://openalex.org/W1999746878","https://openalex.org/W2000494872","https://openalex.org/W2014079103","https://openalex.org/W2021425759","https://openalex.org/W2026350225","https://openalex.org/W2054874912","https://openalex.org/W2064645351","https://openalex.org/W2065127010","https://openalex.org/W2075906776","https://openalex.org/W2084975047","https://openalex.org/W2088090089","https://openalex.org/W2088236202","https://openalex.org/W2090698102","https://openalex.org/W2090911297","https://openalex.org/W2104034609","https://openalex.org/W2164270864","https://openalex.org/W2917362937","https://openalex.org/W3005810761","https://openalex.org/W4211147273","https://openalex.org/W4253687655"],"related_works":["https://openalex.org/W2744716458","https://openalex.org/W1508151251","https://openalex.org/W2165950148","https://openalex.org/W1978417863","https://openalex.org/W2352827678","https://openalex.org/W1972265932","https://openalex.org/W2384561602","https://openalex.org/W2365459235","https://openalex.org/W2366488730","https://openalex.org/W4300101996"],"abstract_inverted_index":{"A":[0],"construction":[1],"of":[2,30,38,56,64,73],"designs":[3,72],"acted":[4],"on":[5],"by":[6],"simple":[7,26],"primitive":[8],"groups":[9],"is":[10],"used":[11],"to":[12],"find":[13],"some":[14],"1-designs":[15],"and":[16,20,43,117],"associated":[17],"self-orthogonal,":[18],"decomposable":[19],"irreducible":[21],"codes":[22,40,60,77],"that":[23],"admit":[24],"the":[25,39,70,74],"group":[27],"${\\rm":[28],"He}$":[29],"Held":[31],"as":[32],"an":[33],"automorphism":[34],"group.":[35],"The":[36],"properties":[37],"are":[41,49],"given":[42],"links":[44],"with":[45,83],"modular":[46],"representation":[47],"theory":[48],"established.":[50],"Further,":[51],"we":[52,78],"introduce":[53],"a":[54],"method":[55],"constructing":[57],"self-orthogonal":[58,66,76],"binary":[59],"from":[61,69],"orbit":[62],"matrices":[63],"weakly":[65],"designs.":[67],"Furthermore,":[68],"support":[71],"obtained":[75],"construct":[79],"strongly":[80],"regular":[81],"graphs":[82],"parameters":[84],"(21,":[85],"10,":[86,102],"3,":[87],"6),":[88,100],"(28,":[89],"12,":[90,94],"6,":[91],"4),":[92],"(49,":[93,97],"5,":[95],"2),":[96,104],"18,":[98],"7,":[99],"(56,":[101],"0,":[103],"(63,":[105],"30,":[106,114],"13,":[107],"15),":[108],"(105,":[109],"32,":[110],"4,":[111],"12),":[112],"(112,":[113],"2,":[115],"10)":[116],"(120,":[118],"42,":[119],"8,":[120],"18).":[121]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}