{"id":"https://openalex.org/W2090195440","doi":"https://doi.org/10.1016/0097-3165(80)90028-x","title":"Integral and rational completions of Hadamard matrices","display_name":"Integral and rational completions of Hadamard matrices","publication_year":1980,"publication_date":"1980-11-01","ids":{"openalex":"https://openalex.org/W2090195440","doi":"https://doi.org/10.1016/0097-3165(80)90028-x","mag":"2090195440"},"language":"en","primary_location":{"id":"doi:10.1016/0097-3165(80)90028-x","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0097-3165(80)90028-x","pdf_url":null,"source":{"id":"https://openalex.org/S128556326","display_name":"Journal of Combinatorial Theory Series A","issn_l":"0097-3165","issn":["0097-3165","1096-0899"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Theory, Series A","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018225600","display_name":"Eric Verheiden","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Eric Verheiden","raw_affiliation_strings":["Aerojet Electrosystems Company, Azusa, California 91702 USA"],"affiliations":[{"raw_affiliation_string":"Aerojet Electrosystems Company, Azusa, California 91702 USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5018225600"],"corresponding_institution_ids":[],"apc_list":{"value":3320,"currency":"USD","value_usd":3320},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.22646357,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"29","issue":"3","first_page":"336","last_page":"345"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9991999864578247,"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":0.9991999864578247,"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/T12504","display_name":"Mathematics and Applications","score":0.9423999786376953,"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"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9082000255584717,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/hadamard-transform","display_name":"Hadamard transform","score":0.8184553980827332},{"id":"https://openalex.org/keywords/hadamard-product","display_name":"Hadamard product","score":0.6574793457984924},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6327709555625916},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.5772270560264587},{"id":"https://openalex.org/keywords/complex-hadamard-matrix","display_name":"Complex Hadamard matrix","score":0.5770101547241211},{"id":"https://openalex.org/keywords/hadamard-matrix","display_name":"Hadamard matrix","score":0.4907022714614868},{"id":"https://openalex.org/keywords/hadamard-three-lines-theorem","display_name":"Hadamard three-lines theorem","score":0.42231664061546326},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4193367660045624},{"id":"https://openalex.org/keywords/row-and-column-spaces","display_name":"Row and column spaces","score":0.4117623567581177},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41170045733451843},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33326417207717896},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3307194113731384},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2781604826450348},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2271377146244049},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.056772202253341675},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.054383933544158936}],"concepts":[{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.8184553980827332},{"id":"https://openalex.org/C90230998","wikidata":"https://www.wikidata.org/wiki/Q3406746","display_name":"Hadamard product","level":3,"score":0.6574793457984924},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6327709555625916},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.5772270560264587},{"id":"https://openalex.org/C6497535","wikidata":"https://www.wikidata.org/wiki/Q5156556","display_name":"Complex Hadamard matrix","level":4,"score":0.5770101547241211},{"id":"https://openalex.org/C30463267","wikidata":"https://www.wikidata.org/wiki/Q1422682","display_name":"Hadamard matrix","level":3,"score":0.4907022714614868},{"id":"https://openalex.org/C68720959","wikidata":"https://www.wikidata.org/wiki/Q3527250","display_name":"Hadamard three-lines theorem","level":4,"score":0.42231664061546326},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4193367660045624},{"id":"https://openalex.org/C104140500","wikidata":"https://www.wikidata.org/wiki/Q2088159","display_name":"Row and column spaces","level":3,"score":0.4117623567581177},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41170045733451843},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33326417207717896},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3307194113731384},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2781604826450348},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2271377146244049},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.056772202253341675},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.054383933544158936},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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:10.1016/0097-3165(80)90028-x","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0097-3165(80)90028-x","pdf_url":null,"source":{"id":"https://openalex.org/S128556326","display_name":"Journal of Combinatorial Theory Series A","issn_l":"0097-3165","issn":["0097-3165","1096-0899"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Theory, Series A","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1983655075","https://openalex.org/W2075692487","https://openalex.org/W2488129653","https://openalex.org/W4239319307"],"related_works":["https://openalex.org/W2138472192","https://openalex.org/W2061168688","https://openalex.org/W2549862220","https://openalex.org/W2790370651","https://openalex.org/W2533841895","https://openalex.org/W2170231972","https://openalex.org/W2376115868","https://openalex.org/W2355675451","https://openalex.org/W2124522323","https://openalex.org/W1976224891"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}