{"id":"https://openalex.org/W7225598149","doi":"https://doi.org/10.5281/zenodo.24061003","title":"On Fourier and Hadamard matrices of prime order","display_name":"On Fourier and Hadamard matrices of prime order","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225598149","doi":"https://doi.org/10.5281/zenodo.24061003"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24061003","doi":"https://doi.org/10.5281/zenodo.24061003","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24061003","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24061003","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025328470","display_name":"Teodor Banica","orcid":"https://orcid.org/0000-0003-4680-0364","observed_orcids":["https://orcid.org/0000-0003-4680-0364"]},"institutions":[{"id":"https://openalex.org/I4210142324","display_name":"CY Cergy Paris Universit\u00e9","ror":"https://ror.org/043htjv09","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210142324"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Banica, Teodor","raw_affiliation_strings":["CY Cergy Paris Universit\u00e9"],"raw_orcid":"https://orcid.org/0000-0003-4680-0364","affiliations":[{"raw_affiliation_string":"CY Cergy Paris Universit\u00e9","institution_ids":["https://openalex.org/I4210142324"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047304570","display_name":"Chat GPT","orcid":"https://orcid.org/0000-0003-0513-5046","observed_orcids":["https://orcid.org/0000-0003-0513-5046"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"GPT, Chat","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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":0.3230000138282776,"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":0.3230000138282776,"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":0.31369999051094055,"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":0.2563000023365021,"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/fourier-matrix","display_name":"Fourier matrix","score":0.890999972820282},{"id":"https://openalex.org/keywords/hadamard-matrices","display_name":"Hadamard matrices","score":0.9409999847412109},{"id":"https://openalex.org/keywords/prime-order","display_name":"prime order","score":0.8270000219345093},{"id":"https://openalex.org/keywords/quadratic-residues","display_name":"quadratic residues","score":0.6050000190734863}],"concepts":[{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.6883000135421753},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6299999952316284},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5788999795913696},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5060999989509583},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.5},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.46860000491142273},{"id":"https://openalex.org/C30463267","wikidata":"https://www.wikidata.org/wiki/Q1422682","display_name":"Hadamard matrix","level":3,"score":0.4544000029563904},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42149999737739563},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.38999998569488525},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.3747999966144562},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.35839998722076416},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3537999987602234},{"id":"https://openalex.org/C7720571","wikidata":"https://www.wikidata.org/wiki/Q1136880","display_name":"Power of two","level":2,"score":0.349700003862381},{"id":"https://openalex.org/C121334634","wikidata":"https://www.wikidata.org/wiki/Q5637579","display_name":"Hadamard's maximal determinant problem","level":5,"score":0.3458000123500824},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.3391000032424927},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.33869999647140503},{"id":"https://openalex.org/C6497535","wikidata":"https://www.wikidata.org/wiki/Q5156556","display_name":"Complex Hadamard matrix","level":4,"score":0.33550000190734863},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3224000036716461},{"id":"https://openalex.org/C104140500","wikidata":"https://www.wikidata.org/wiki/Q2088159","display_name":"Row and column spaces","level":3,"score":0.30169999599456787},{"id":"https://openalex.org/C103945485","wikidata":"https://www.wikidata.org/wiki/Q5204933","display_name":"DFT matrix","level":5,"score":0.2937000095844269},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28859999775886536},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.2791999876499176},{"id":"https://openalex.org/C519991488","wikidata":"https://www.wikidata.org/wiki/Q28865","display_name":"Python (programming language)","level":2,"score":0.27079999446868896},{"id":"https://openalex.org/C2781020372","wikidata":"https://www.wikidata.org/wiki/Q533093","display_name":"On the fly","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.25699999928474426}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24061003","doi":"https://doi.org/10.5281/zenodo.24061003","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24061003","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.24061004","doi":"https://doi.org/10.5281/zenodo.24061004","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24061004","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"doi:10.5281/zenodo.24061003","doi":"https://doi.org/10.5281/zenodo.24061003","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24061003","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2975319550","https://openalex.org/W1970039295","https://openalex.org/W1565641324","https://openalex.org/W7213749213","https://openalex.org/W6910638571","https://openalex.org/W4293691048","https://openalex.org/W1989019857","https://openalex.org/W2012122938","https://openalex.org/W7203776433","https://openalex.org/W2950407681"],"abstract_inverted_index":{"We":[0,45],"study":[1],"how":[2],"much":[3],"of":[4,8],"the":[5,26,35,39,70,76,85,95,101,107],"Fourier":[6,40],"matrix":[7,41],"prime":[9,64],"order":[10],"is":[11],"needed":[12],"to":[13,43],"recognize":[14],"it":[15],"among":[16],"regular":[17],"or":[18],"Butson":[19],"Hadamard":[20],"matrices.":[21],"For":[22],"every":[23,62],"odd":[24,63],"prime,":[25],"block":[27],"whose":[28],"rows":[29],"and":[30,52,75,78,82,97,99,111],"columns":[31],"are":[32],"indexed":[33],"by":[34],"nonzero":[36],"squares":[37],"determines":[38],"up":[42],"equivalence.":[44],"also":[46],"prove":[47],"an":[48],"entrywise":[49],"power":[50],"dichotomy":[51],"obtain":[53],"a":[54,58],"recognition":[55],"criterion":[56],"from":[57],"two-orbit":[59],"symmetry":[60],"at":[61],"through":[65],"109.":[66],"The":[67,104],"repository":[68],"contains":[69],"paper,":[71],"its":[72],"LaTeX":[73],"source,":[74],"Python":[77],"C++":[79],"programs,":[80],"inputs,":[81],"certificates":[83],"for":[84],"finite":[86],"calculations.":[87],"ChatGPT":[88],"assisted":[89],"with":[90],"developing":[91],"mathematical":[92],"arguments,":[93],"drafting":[94],"manuscript,":[96],"writing":[98],"checking":[100],"computational":[102],"code.":[103],"paper":[105],"carries":[106],"byline":[108],"Teo":[109],"B":[110],"Chat":[112],"GPT.":[113]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}