{"id":"https://openalex.org/W4411745093","doi":"https://doi.org/10.1007/s10623-025-01676-y","title":"Unbiased weighing matrices of weight 9","display_name":"Unbiased weighing matrices of weight 9","publication_year":2025,"publication_date":"2025-06-28","ids":{"openalex":"https://openalex.org/W4411745093","doi":"https://doi.org/10.1007/s10623-025-01676-y"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-025-01676-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-025-01676-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-025-01676-y.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","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/s10623-025-01676-y.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019966275","display_name":"Makoto Araya","orcid":"https://orcid.org/0000-0002-9935-038X"},"institutions":[{"id":"https://openalex.org/I1298590031","display_name":"Shizuoka University","ror":"https://ror.org/01w6wtk13","country_code":"JP","type":"education","lineage":["https://openalex.org/I1298590031"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Makoto Araya","raw_affiliation_strings":["Department of Computer Science, Shizuoka University, Hamamatsu, 432-8011, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Shizuoka University, Hamamatsu, 432-8011, Japan","institution_ids":["https://openalex.org/I1298590031"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108192229","display_name":"Masaaki Harada","orcid":null},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Masaaki Harada","raw_affiliation_strings":["Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan","institution_ids":["https://openalex.org/I201537933"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028347422","display_name":"Hadi Kharaghani","orcid":"https://orcid.org/0000-0003-0115-7117"},"institutions":[{"id":"https://openalex.org/I107949126","display_name":"University of Lethbridge","ror":"https://ror.org/044j76961","country_code":"CA","type":"education","lineage":["https://openalex.org/I107949126"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Hadi Kharaghani","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, T1K 3M4, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, T1K 3M4, Canada","institution_ids":["https://openalex.org/I107949126"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036298064","display_name":"Sho Suda","orcid":"https://orcid.org/0000-0002-5280-2668"},"institutions":[{"id":"https://openalex.org/I443798","display_name":"National Defense Academy of Japan","ror":"https://ror.org/05xszy717","country_code":"JP","type":"education","lineage":["https://openalex.org/I443798"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Sho Suda","raw_affiliation_strings":["Department of Mathematics, National Defense Academy of Japan, Yokosuka, Kanagawa, 239-8686, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Defense Academy of Japan, Yokosuka, Kanagawa, 239-8686, Japan","institution_ids":["https://openalex.org/I443798"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032354006","display_name":"Wenbao Yu","orcid":"https://orcid.org/0000-0001-8860-2644"},"institutions":[{"id":"https://openalex.org/I22265921","display_name":"National Central University","ror":"https://ror.org/00944ve71","country_code":"TW","type":"education","lineage":["https://openalex.org/I22265921"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Wei-Hsuan Yu","raw_affiliation_strings":["Mathematics Department, National Central University, Taoy\u00fcan, 32001, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, National Central University, Taoy\u00fcan, 32001, Taiwan","institution_ids":["https://openalex.org/I22265921"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5108192229"],"corresponding_institution_ids":["https://openalex.org/I201537933"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":1.2644,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.84405109,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"93","issue":"10","first_page":"4235","last_page":"4273"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9858999848365784,"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/T11383","display_name":"Advanced Antenna and Metasurface Technologies","score":0.9754999876022339,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/mathematics","display_name":"Mathematics","score":0.8328133821487427},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4839182496070862},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3333968222141266},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32643288373947144}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8328133821487427},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4839182496070862},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3333968222141266},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32643288373947144}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10623-025-01676-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-025-01676-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-025-01676-y.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10623-025-01676-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-025-01676-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-025-01676-y.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1426543890","display_name":"Evolution of Combinatorial Coding Theory","funder_award_id":"23K25784","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8193353624","display_name":"Algebraic and geometric progress by graph representations of combinatorial structures","funder_award_id":"21K03350","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G937052642","display_name":"A study of complex spherical codes and designs by algebraic methods","funder_award_id":"22K03410","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320324720","display_name":"Soochow University","ror":"https://ror.org/05t8y2r12"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411745093.pdf","grobid_xml":"https://content.openalex.org/works/W4411745093.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1976201283","https://openalex.org/W1976677460","https://openalex.org/W2006550031","https://openalex.org/W2007408675","https://openalex.org/W2037306962","https://openalex.org/W2055726455","https://openalex.org/W2085280930","https://openalex.org/W2091341249","https://openalex.org/W2094171408","https://openalex.org/W2101504517","https://openalex.org/W2111381006","https://openalex.org/W2133866430","https://openalex.org/W2147461090","https://openalex.org/W2408532372","https://openalex.org/W2584020404","https://openalex.org/W4205545339","https://openalex.org/W4232894208","https://openalex.org/W4394934447","https://openalex.org/W4408734169"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"investigate":[2],"unbiased":[3,41,76],"weighing":[4,42,77],"matrices":[5,43,78],"of":[6,39,44,75],"weight":[7,48],"9":[8],"and":[9,47,64],"provide":[10],"a":[11,72],"construction":[12],"method":[13],"using":[14],"mutually":[15,40],"suitable":[16],"Latin":[17],"squares.":[18],"For":[19],"$$n":[20],"\\le":[21],"16$$":[22],"<mml:math":[23],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[24],"<mml:mrow>":[25],"<mml:mi>n</mml:mi>":[26],"<mml:mo>\u2264</mml:mo>":[27],"<mml:mn>16</mml:mn>":[28],"</mml:mrow>":[29],"</mml:math>":[30],",":[31],"we":[32],"determine":[33],"the":[34,57,67],"maximum":[35,73],"size":[36],"among":[37],"sets":[38],"order":[45,59,69],"n":[46],"9.":[49],"Notably,":[50],"our":[51],"findings":[52],"reveal":[53],"that":[54],"13":[55],"is":[56,66,79],"smallest":[58],"where":[60],"such":[61],"pairs":[62],"exist,":[63],"16":[65],"first":[68],"for":[70],"which":[71],"class":[74],"found.":[80]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}