{"id":"https://openalex.org/W2940924876","doi":"https://doi.org/10.1002/jcd.21664","title":"Constructing cocyclic Hadamard matrices of order 4p","display_name":"Constructing cocyclic Hadamard matrices of order 4p","publication_year":2019,"publication_date":"2019-08-27","ids":{"openalex":"https://openalex.org/W2940924876","doi":"https://doi.org/10.1002/jcd.21664","mag":"2940924876"},"language":"en","primary_location":{"id":"doi:10.1002/jcd.21664","doi":"https://doi.org/10.1002/jcd.21664","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jcd.21664","pdf_url":null,"source":{"id":"https://openalex.org/S8494942","display_name":"Journal of Combinatorial Designs","issn_l":"1063-8539","issn":["1063-8539","1520-6610"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Designs","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1904.11460","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073791050","display_name":"Santiago Barrera Acevedo","orcid":"https://orcid.org/0000-0001-5793-3600","observed_orcids":["https://orcid.org/0000-0001-5793-3600"]},"institutions":[{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Santiago Barrera Acevedo","raw_affiliation_strings":["School of Mathematics Monash University Clayton Victoria Australia"],"raw_orcid":"https://orcid.org/0000-0001-5793-3600","affiliations":[{"raw_affiliation_string":"School of Mathematics Monash University Clayton Victoria Australia","institution_ids":["https://openalex.org/I56590836"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045472759","display_name":"Padraig \u00d3 Cath\u00e1in","orcid":"https://orcid.org/0000-0002-7963-9688","observed_orcids":["https://orcid.org/0000-0002-7963-9688"]},"institutions":[{"id":"https://openalex.org/I107077323","display_name":"Worcester Polytechnic Institute","ror":"https://ror.org/05ejpqr48","country_code":"US","type":"education","lineage":["https://openalex.org/I107077323"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Padraig \u00d3 Cath\u00e1in","raw_affiliation_strings":["Mathematical Sciences Department Worcester Polytechnic Institute Worcester Massachusetts"],"raw_orcid":"https://orcid.org/0000-0002-7963-9688","affiliations":[{"raw_affiliation_string":"Mathematical Sciences Department Worcester Polytechnic Institute Worcester Massachusetts","institution_ids":["https://openalex.org/I107077323"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008145013","display_name":"Heiko Dietrich","orcid":"https://orcid.org/0000-0002-1996-9650","observed_orcids":["https://orcid.org/0000-0002-1996-9650"]},"institutions":[{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Heiko Dietrich","raw_affiliation_strings":["School of Mathematics Monash University Clayton Victoria Australia"],"raw_orcid":"https://orcid.org/0000-0002-1996-9650","affiliations":[{"raw_affiliation_string":"School of Mathematics Monash University Clayton Victoria Australia","institution_ids":["https://openalex.org/I56590836"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073791050"],"corresponding_institution_ids":["https://openalex.org/I56590836"],"apc_list":{"value":2500,"currency":"USD","value_usd":2500},"apc_paid":null,"fwci":0.6235,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.54713147,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":96},"biblio":{"volume":"27","issue":"11","first_page":"627","last_page":"642"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.6488999724388123,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.6488999724388123,"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/T10849","display_name":"Finite Group Theory Research","score":0.1736000031232834,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.14149999618530273,"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/hadamard-matrices","display_name":"Hadamard matrices","score":0.9559999704360962},{"id":"https://openalex.org/keywords/relative-difference-sets","display_name":"relative difference sets","score":0.6930000185966492},{"id":"https://openalex.org/keywords/classifiers","display_name":"machine learning classifiers","score":0.8090000152587891},{"id":"https://openalex.org/keywords/block-structure","display_name":"block structure","score":0.5329999923706055},{"id":"https://openalex.org/keywords/prime-power-order","display_name":"prime power order","score":0.3930000066757202}],"concepts":[{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.7893158197402954},{"id":"https://openalex.org/C30463267","wikidata":"https://www.wikidata.org/wiki/Q1422682","display_name":"Hadamard matrix","level":3,"score":0.6970811486244202},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6939177513122559},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6796413064002991},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.558249831199646},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5292693376541138},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4929053783416748},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4727904498577118},{"id":"https://openalex.org/C6497535","wikidata":"https://www.wikidata.org/wiki/Q5156556","display_name":"Complex Hadamard matrix","level":4,"score":0.4611051678657532},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4587209224700928},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4523899257183075},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.327727347612381},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11804762482643127},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.055798113346099854},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1002/jcd.21664","doi":"https://doi.org/10.1002/jcd.21664","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jcd.21664","pdf_url":null,"source":{"id":"https://openalex.org/S8494942","display_name":"Journal of Combinatorial Designs","issn_l":"1063-8539","issn":["1063-8539","1520-6610"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Designs","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1904.11460","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1904.11460","pdf_url":"https://arxiv.org/pdf/1904.11460","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,"listed_in":[],"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:2940924876","doi":null,"is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1904.11460","pdf_url":null,"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,"listed_in":[],"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.1904.11460","doi":"https://doi.org/10.48550/arxiv.1904.11460","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1904.11460","pdf_url":null,"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,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1904.11460","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1904.11460","pdf_url":"https://arxiv.org/pdf/1904.11460","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,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2940924876.pdf","grobid_xml":"https://content.openalex.org/works/W2940924876.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W401986301","https://openalex.org/W593444048","https://openalex.org/W1532853593","https://openalex.org/W1976677460","https://openalex.org/W1999413354","https://openalex.org/W2003940980","https://openalex.org/W2008952375","https://openalex.org/W2021875115","https://openalex.org/W2024144406","https://openalex.org/W2035396889","https://openalex.org/W2042826512","https://openalex.org/W2050803168","https://openalex.org/W2075412945","https://openalex.org/W2080193232","https://openalex.org/W2081376314","https://openalex.org/W2098201534","https://openalex.org/W2131599704","https://openalex.org/W2902744720","https://openalex.org/W2910516124","https://openalex.org/W4238777108"],"related_works":["https://openalex.org/W2003940980","https://openalex.org/W4410098611","https://openalex.org/W2082156999","https://openalex.org/W2950407681","https://openalex.org/W2902744720","https://openalex.org/W2098201534","https://openalex.org/W7212017870","https://openalex.org/W2132282830","https://openalex.org/W2054788067","https://openalex.org/W2086181739"],"abstract_inverted_index":{"Abstract":[0],"Cocyclic":[1],"Hadamard":[2,16],"matrices":[3,17],"(CHMs)":[4],"were":[5],"introduced":[6],"by":[7],"de":[8,64],"Launey":[9,65],"and":[10,25,66,85,114],"Horadam":[11],"as":[12],"a":[13,28,70,78,87,103,128],"class":[14],"of":[15,33,42,50,53,61,63,75,97,107,123],"(HMs)":[18],"with":[19,77,99,105],"interesting":[20],"algebraic":[21],"properties.":[22],"\u00d3":[23],"Cath\u00e1in":[24],"R\u00f6der":[26],"described":[27],"classification":[29,49,71,88],"algorithm":[30,72],"for":[31,73,89],"CHMs":[32,52,74],"order":[34,43,54,76,98,124],"based":[35],"on":[36],"relative":[37],"difference":[38],"sets":[39],"in":[40],"groups":[41],";":[44],"this":[45],"led":[46],"to":[47,102,127],"the":[48,59],"all":[51],"at":[55],"most":[56],"36.":[57],"On":[58],"basis":[60],"work":[62],"Flannery,":[67],"we":[68,80],"describe":[69],"prime;":[79],"prove":[81],"refined":[82],"structure":[83],"results":[84],"provide":[86],".":[90],"Our":[91],"analysis":[92],"shows":[93],"that":[94],"every":[95,121],"CHM":[96,122],"is":[100,125],"equivalent":[101,126],"HM":[104],"one":[106],"five":[108],"distinct":[109],"block":[110],"structures,":[111],"including":[112],"Williamson\u2010type":[113,129],"(transposed)":[115,131],"Ito":[116,132],"matrices.":[117],"If":[118],",":[119],"then":[120],"or":[130],"matrix.":[133]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2019-05-03T00:00:00"}