{"id":"https://openalex.org/W2891231750","doi":"https://doi.org/10.1007/s11786-018-0379-8","title":"Extension of the Set of Complex Hadamard Matrices of Size\u00a08","display_name":"Extension of the Set of Complex Hadamard Matrices of Size\u00a08","publication_year":2018,"publication_date":"2018-09-19","ids":{"openalex":"https://openalex.org/W2891231750","doi":"https://doi.org/10.1007/s11786-018-0379-8","mag":"2891231750"},"language":"en","primary_location":{"id":"doi:10.1007/s11786-018-0379-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11786-018-0379-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11786-018-0379-8.pdf","source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11786-018-0379-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071398167","display_name":"Wojciech Bruzda","orcid":"https://orcid.org/0000-0001-9743-7927"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]},{"id":"https://openalex.org/I4210086947","display_name":"Institute of Physics","ror":"https://ror.org/000sfad56","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210086947","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Wojciech T. Bruzda","raw_affiliation_strings":["Institute of Physics, Jagiellonian University, Krak\u00f3w, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Physics, Jagiellonian University, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746","https://openalex.org/I4210086947"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5071398167"],"corresponding_institution_ids":["https://openalex.org/I126596746","https://openalex.org/I4210086947"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.07904241,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"12","issue":"4","first_page":"459","last_page":"464"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9998999834060669,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9765999913215637,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T12504","display_name":"Mathematics and Applications","score":0.9581000208854675,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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-transform","display_name":"Hadamard transform","score":0.8351516723632812},{"id":"https://openalex.org/keywords/complex-hadamard-matrix","display_name":"Complex Hadamard matrix","score":0.8349306583404541},{"id":"https://openalex.org/keywords/hadamard-matrix","display_name":"Hadamard matrix","score":0.7732083201408386},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7158111929893494},{"id":"https://openalex.org/keywords/hadamards-maximal-determinant-problem","display_name":"Hadamard's maximal determinant problem","score":0.6382863521575928},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6100726127624512},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5698947310447693},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5095372796058655},{"id":"https://openalex.org/keywords/hadamards-inequality","display_name":"Hadamard's inequality","score":0.5064114332199097},{"id":"https://openalex.org/keywords/identity-matrix","display_name":"Identity matrix","score":0.48494794964790344},{"id":"https://openalex.org/keywords/complex-matrix","display_name":"Complex matrix","score":0.41188687086105347},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3479663133621216},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31712448596954346},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.14117223024368286},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12462952733039856},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09249496459960938},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.05932050943374634}],"concepts":[{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.8351516723632812},{"id":"https://openalex.org/C6497535","wikidata":"https://www.wikidata.org/wiki/Q5156556","display_name":"Complex Hadamard matrix","level":4,"score":0.8349306583404541},{"id":"https://openalex.org/C30463267","wikidata":"https://www.wikidata.org/wiki/Q1422682","display_name":"Hadamard matrix","level":3,"score":0.7732083201408386},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7158111929893494},{"id":"https://openalex.org/C121334634","wikidata":"https://www.wikidata.org/wiki/Q5637579","display_name":"Hadamard's maximal determinant problem","level":5,"score":0.6382863521575928},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6100726127624512},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5698947310447693},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5095372796058655},{"id":"https://openalex.org/C31021346","wikidata":"https://www.wikidata.org/wiki/Q1365087","display_name":"Hadamard's inequality","level":4,"score":0.5064114332199097},{"id":"https://openalex.org/C134567657","wikidata":"https://www.wikidata.org/wiki/Q193794","display_name":"Identity matrix","level":3,"score":0.48494794964790344},{"id":"https://openalex.org/C2988629283","wikidata":"https://www.wikidata.org/wiki/Q44337","display_name":"Complex matrix","level":2,"score":0.41188687086105347},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3479663133621216},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31712448596954346},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.14117223024368286},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12462952733039856},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09249496459960938},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.05932050943374634},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11786-018-0379-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11786-018-0379-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11786-018-0379-8.pdf","source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11786-018-0379-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11786-018-0379-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11786-018-0379-8.pdf","source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1224756538","display_name":null,"funder_award_id":"DEC-2015/18/A ST2/00274","funder_id":"https://openalex.org/F4320322511","funder_display_name":"Narodowe Centrum Nauki"},{"id":"https://openalex.org/G1711689202","display_name":null,"funder_award_id":"2015/18/A/ST2/00274","funder_id":"https://openalex.org/F4320322511","funder_display_name":"Narodowe Centrum Nauki"},{"id":"https://openalex.org/G2485725195","display_name":null,"funder_award_id":"A/ST2/00274","funder_id":"https://openalex.org/F4320322511","funder_display_name":"Narodowe Centrum Nauki"}],"funders":[{"id":"https://openalex.org/F4320322511","display_name":"Narodowe Centrum Nauki","ror":"https://ror.org/03ha2q922"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2891231750.pdf","grobid_xml":"https://content.openalex.org/works/W2891231750.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1983182028","https://openalex.org/W2009600348","https://openalex.org/W2031422325","https://openalex.org/W2039842791","https://openalex.org/W2046938896","https://openalex.org/W2047595535","https://openalex.org/W2058559947","https://openalex.org/W2064610453","https://openalex.org/W2080931848","https://openalex.org/W2081226011","https://openalex.org/W2111925490","https://openalex.org/W2123131736","https://openalex.org/W2123862442","https://openalex.org/W2132641463","https://openalex.org/W2136385664","https://openalex.org/W2334323920","https://openalex.org/W2730967542","https://openalex.org/W2963632982","https://openalex.org/W3100900940","https://openalex.org/W3103642445","https://openalex.org/W3105431454","https://openalex.org/W6825279867"],"related_works":["https://openalex.org/W1976224891","https://openalex.org/W2026768906","https://openalex.org/W2138472192","https://openalex.org/W4226106482","https://openalex.org/W1971692815","https://openalex.org/W2355675451","https://openalex.org/W2124522323","https://openalex.org/W2072949187","https://openalex.org/W2740594951","https://openalex.org/W2003940980"],"abstract_inverted_index":{"A":[0],"complex":[1,39,59],"Hadamard":[2,40,60],"matrix":[3,8,30,68],"is":[4,27],"defined":[5],"as":[6],"a":[7,53,63],"H":[9],"which":[10],"fulfills":[11],"two":[12,49],"conditions,":[13],"$$|H_{j,k}|=1$$":[14],"for":[15],"all":[16],"j":[17],"and":[18,20,47,62,66],"k":[19],"$$HH^{*}=N":[21],"\\mathbb":[22],"{I}_N$$":[23,26],"where":[24],"$$\\mathbb":[25],"an":[28],"identity":[29],"of":[31,38,44,58],"size":[32,45],"N.":[33],"We":[34],"explore":[35],"the":[36],"set":[37],"matrices":[41,61],"$$\\mathcal":[42],"{H}_N$$":[43],"$$N=8$$":[46],"present":[48],"previously":[50],"unknown":[51],"structures:":[52],"one-parametric,":[54],"non-affine":[55],"family":[56],"$$T_8^{(1)}$$":[57],"single":[64],"symmetric":[65],"isolated":[67],"$$A_8^{(0)}$$":[69],".":[70]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
