{"id":"https://openalex.org/W7223155683","doi":"https://doi.org/10.48550/arxiv.2610.27175","title":"Recent progress in the construction of Hadamard matrices","display_name":"Recent progress in the construction of Hadamard matrices","publication_year":2026,"publication_date":"2026-10-19","ids":{"openalex":"https://openalex.org/W7223155683","doi":"https://doi.org/10.48550/arxiv.2610.27175"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.27175","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27175","pdf_url":"https://arxiv.org/pdf/2610.27175","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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.27175","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091026595","display_name":"Ronan Egan","orcid":"https://orcid.org/0000-0001-6010-116X","observed_orcids":["https://orcid.org/0000-0001-6010-116X"]},"institutions":[{"id":"https://openalex.org/I42934936","display_name":"Dublin City University","ror":"https://ror.org/04a1a1e81","country_code":"IE","type":"education","lineage":["https://openalex.org/I42934936"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Egan, Ronan","raw_affiliation_strings":["School of Mathematical Sciences , Dublin City University , Ireland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Dublin City University , Ireland","institution_ids":["https://openalex.org/I42934936"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069151859","display_name":"Ilias Kotsireas","orcid":"https://orcid.org/0000-0003-2126-8383","observed_orcids":["https://orcid.org/0000-0003-2126-8383"]},"institutions":[{"id":"https://openalex.org/I75381157","display_name":"Wilfrid Laurier University","ror":"https://ror.org/00fn7gb05","country_code":"CA","type":"education","lineage":["https://openalex.org/I75381157"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Kotsireas, Ilias","raw_affiliation_strings":["Wilfrid Laurier University , Waterloo , Ontario , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wilfrid Laurier University , Waterloo , Ontario , Canada","institution_ids":["https://openalex.org/I75381157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007645551","display_name":"Stephen London","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1925986","display_name":"Loyola University Chicago","ror":"https://ror.org/04b6x2g63","country_code":"US","type":"education","lineage":["https://openalex.org/I1925986"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"London, Stephen","raw_affiliation_strings":["Loyola University , Chicago , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Loyola University , Chicago , USA","institution_ids":["https://openalex.org/I1925986"]}]},{"author_position":"last","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":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cath\u00e1in, P\u00e1draig \u00d3","raw_affiliation_strings":["\u00dadar\u00e1s na Gaeltachta , Ireland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00dadar\u00e1s na Gaeltachta , Ireland","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.49559998512268066,"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":0.49559998512268066,"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":0.38499999046325684,"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":0.051600001752376556,"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":1.0},{"id":"https://openalex.org/keywords/hadamard-matrix-construction","display_name":"Hadamard matrix construction","score":0.7960000038146973},{"id":"https://openalex.org/keywords/open-order","display_name":"open order","score":0.5460000038146973},{"id":"https://openalex.org/keywords/open-problems","display_name":"open problems","score":0.3540000021457672}],"concepts":[{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.8123999834060669},{"id":"https://openalex.org/C30463267","wikidata":"https://www.wikidata.org/wiki/Q1422682","display_name":"Hadamard matrix","level":3,"score":0.8034999966621399},{"id":"https://openalex.org/C31021346","wikidata":"https://www.wikidata.org/wiki/Q1365087","display_name":"Hadamard's inequality","level":4,"score":0.770799994468689},{"id":"https://openalex.org/C121334634","wikidata":"https://www.wikidata.org/wiki/Q5637579","display_name":"Hadamard's maximal determinant problem","level":5,"score":0.7511000037193298},{"id":"https://openalex.org/C6497535","wikidata":"https://www.wikidata.org/wiki/Q5156556","display_name":"Complex Hadamard matrix","level":4,"score":0.7311999797821045},{"id":"https://openalex.org/C68720959","wikidata":"https://www.wikidata.org/wiki/Q3527250","display_name":"Hadamard three-lines theorem","level":4,"score":0.7224000096321106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6956999897956848},{"id":"https://openalex.org/C90230998","wikidata":"https://www.wikidata.org/wiki/Q3406746","display_name":"Hadamard product","level":3,"score":0.6140999794006348},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48010000586509705},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4772000014781952},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4505000114440918},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.43849998712539673},{"id":"https://openalex.org/C35222485","wikidata":"https://www.wikidata.org/wiki/Q729359","display_name":"Hadamard three-circle theorem","level":5,"score":0.4090999960899353},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.38109999895095825},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3601999878883362},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.2996000051498413},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.29649999737739563},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.28690001368522644}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.27175","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27175","pdf_url":"https://arxiv.org/pdf/2610.27175","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":"doi:10.48550/arxiv.2610.27175","doi":"https://doi.org/10.48550/arxiv.2610.27175","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.27175","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.27175","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27175","pdf_url":"https://arxiv.org/pdf/2610.27175","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/W7223155683.pdf","grobid_xml":"https://content.openalex.org/works/W7223155683.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7125093963","https://openalex.org/W7097963314","https://openalex.org/W154709419","https://openalex.org/W2016791134","https://openalex.org/W2060079309","https://openalex.org/W2265174874","https://openalex.org/W2949923959","https://openalex.org/W2076819986","https://openalex.org/W2056127839","https://openalex.org/W2701973148"],"abstract_inverted_index":{"A":[0],"Hadamard":[1,16,52,82,95,106],"matrix":[2,6,96],"is":[3,97],"a":[4,121],"square":[5],"with":[7,120],"entries":[8],"$\\pm":[9],"1$":[10],"whose":[11],"rows":[12],"are":[13,18],"mutually":[14],"orthogonal.":[15],"matrices":[17,53,83,107],"conjectured":[19],"to":[20,90],"exist":[21],"at":[22,54,60,92,108],"every":[23],"order":[24,42],"divisible":[25],"by":[26],"$4$;":[27],"for":[28],"approximately":[29],"the":[30,34,55,72,79,86,115],"last":[31],"twenty":[32],"years,":[33],"smallest":[35],"open":[36,113,124],"case":[37],"of":[38,81,123],"this":[39,66,102],"conjecture":[40],"was":[41,63],"668.":[43],"In":[44,65,100],"August":[45],"2026,":[46],"Alp\u00f6ge,":[47],"Voinov":[48],"and":[49,70,84],"Reynolds-Haertle":[50],"announced":[51],"twelve":[56],"orders":[57,88,110],"below":[58],"$2000$":[59],"which":[61,93],"none":[62],"known.":[64,99],"paper":[67],"we":[68,104],"verify":[69],"analyse":[71],"claimed":[73],"matrices.":[74],"We":[75,118],"survey":[76],"results":[77],"on":[78],"existence":[80],"list":[85,122],"$85$":[87],"up":[89],"$10\\,000$":[91],"no":[94],"currently":[98],"pursuing":[101],"work":[103],"constructed":[105],"sixteen":[109],"that":[111],"were":[112],"in":[114],"published":[116],"literature.":[117],"conclude":[119],"problems.":[125]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-22T00:00:00"}
