{"id":"https://openalex.org/W7204113716","doi":"https://doi.org/10.48550/arxiv.2608.21048","title":"A Method of Construction of Pairwise Additive Balanced Incomplete Block Designs","display_name":"A Method of Construction of Pairwise Additive Balanced Incomplete Block Designs","publication_year":2026,"publication_date":"2026-08-21","ids":{"openalex":"https://openalex.org/W7204113716","doi":"https://doi.org/10.48550/arxiv.2608.21048"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.21048","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.21048","pdf_url":"https://arxiv.org/pdf/2608.21048","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/2608.21048","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009605315","display_name":"Kazuki Matsubara","orcid":"https://orcid.org/0000-0001-5188-8028","observed_orcids":["https://orcid.org/0000-0001-5188-8028"]},"institutions":[{"id":"https://openalex.org/I72253084","display_name":"Saitama University","ror":"https://ror.org/02evnh647","country_code":"JP","type":"education","lineage":["https://openalex.org/I72253084"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Matsubara, Kazuki","raw_affiliation_strings":["Faculty of Education , Saitama University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Education , Saitama University","institution_ids":["https://openalex.org/I72253084"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017700355","display_name":"Satoru Kadowaki","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210131413","display_name":"National Institute of Technology, Matsue College","ror":"https://ror.org/03qhht705","country_code":"JP","type":"education","lineage":["https://openalex.org/I4210120810","https://openalex.org/I4210131413"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kadowaki, Satoru","raw_affiliation_strings":["Department of Mathematics , Matsue College of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Matsue College of Technology","institution_ids":["https://openalex.org/I4210131413"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.7318999767303467,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.7318999767303467,"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":0.12160000205039978,"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/T11130","display_name":"Coding theory and cryptography","score":0.06620000302791595,"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/generalized-hadamard-matrices","display_name":"generalized Hadamard matrices","score":0.9929999709129333},{"id":"https://openalex.org/keywords/design-construction","display_name":"design construction","score":0.6629999876022339},{"id":"https://openalex.org/keywords/existence-of-designs","display_name":"existence of designs","score":0.6489999890327454}],"concepts":[{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.92330002784729},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7572000026702881},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6940000057220459},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.6644999980926514},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6001999974250793},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4196000099182129},{"id":"https://openalex.org/C689293","wikidata":"https://www.wikidata.org/wiki/Q751484","display_name":"Block design","level":2,"score":0.41510000824928284},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4000000059604645},{"id":"https://openalex.org/C30463267","wikidata":"https://www.wikidata.org/wiki/Q1422682","display_name":"Hadamard matrix","level":3,"score":0.365200012922287},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.3463999927043915},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3416000008583069},{"id":"https://openalex.org/C2983050975","wikidata":"https://www.wikidata.org/wiki/Q88287214","display_name":"Block structure","level":3,"score":0.3375999927520752},{"id":"https://openalex.org/C68720959","wikidata":"https://www.wikidata.org/wiki/Q3527250","display_name":"Hadamard three-lines theorem","level":4,"score":0.31459999084472656},{"id":"https://openalex.org/C114928208","wikidata":"https://www.wikidata.org/wiki/Q17104952","display_name":"Pairwise independence","level":5,"score":0.30399999022483826}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.21048","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.21048","pdf_url":"https://arxiv.org/pdf/2608.21048","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.2608.21048","doi":"https://doi.org/10.48550/arxiv.2608.21048","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.21048","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.21048","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.21048","pdf_url":"https://arxiv.org/pdf/2608.21048","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":[{"id":"https://openalex.org/G854118414","display_name":"\u96e2\u6563\u6570\u5b66\u3092\u984c\u6750\u3068\u3057\u305f\u63a2\u7a76\u578b\u5b66\u7fd2\u652f\u63f4\u30b7\u30b9\u30c6\u30e0\u306e\u69cb\u7bc9\u306b\u95a2\u3059\u308b\u5b9f\u8a3c\u7684\u7814\u7a76","funder_award_id":"23K02359","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"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/W7204113716.pdf","grobid_xml":"https://content.openalex.org/works/W7204113716.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1998950781","https://openalex.org/W2151534966","https://openalex.org/W1978764510","https://openalex.org/W2891802340","https://openalex.org/W7100792117","https://openalex.org/W2316001672","https://openalex.org/W7100118737","https://openalex.org/W4409700199","https://openalex.org/W2043119260","https://openalex.org/W2736151188"],"abstract_inverted_index":{"The":[0],"existence":[1,79,102],"of":[2,4,35,64,91],"sets":[3,100],"balanced":[5],"incomplete":[6],"block":[7],"(BIB)":[8],"designs":[9,38,51,68,97],"with":[10,77,98],"pairwise":[11,14,65,92],"additivity,":[12],"called":[13],"additive":[15,66,93],"BIB":[16,67,94],"designs,":[17,95],"has":[18],"been":[19],"studied":[20],"through":[21],"direct":[22],"and":[23],"recursive":[24],"constructions":[25],"in":[26],"the":[27,61,74],"literature.":[28],"This":[29],"paper":[30],"presents":[31],"a":[32],"new":[33,88],"method":[34],"constructing":[36],"such":[37],"from":[39,54,69],"affine":[40],"resolvable":[41],"semi-regular":[42],"group":[43],"divisible":[44],"(ARSRGD)":[45],"designs.":[46],"Since":[47],"many":[48],"known":[49,78],"ARSRGD":[50],"are":[52],"obtained":[53],"generalized":[55,70,82],"Hadamard":[56,71,83],"matrices,":[57,84],"we":[58,85],"also":[59],"describe":[60],"corresponding":[62],"construction":[63,75],"matrices.":[72],"Using":[73],"together":[76],"results":[80],"for":[81],"obtain":[86],"several":[87],"infinite":[89],"series":[90],"including":[96],"parameter":[99],"whose":[101],"was":[103],"previously":[104],"unknown.":[105]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-25T00:00:00"}
