{"id":"https://openalex.org/W1731792027","doi":"https://doi.org/10.3934/amc.2017030","title":"A multi-dimensional block-circulant perfect array construction","display_name":"A multi-dimensional block-circulant perfect array construction","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W1731792027","doi":"https://doi.org/10.3934/amc.2017030","mag":"1731792027"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2017030","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2017030","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/amc.2017030","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002367174","display_name":"Samuel T. Blake","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Samuel T. Blake","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Andrew Z. Tirkel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrew Z. Tirkel","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002367174"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00053048,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":"2","first_page":"367","last_page":"371"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9908000230789185,"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":0.9908000230789185,"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/T11946","display_name":"Antenna Design and Optimization","score":0.98089998960495,"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"}},{"id":"https://openalex.org/T10575","display_name":"Wireless Communication Networks Research","score":0.9646000266075134,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.9112993478775024},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.900708794593811},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7552546262741089},{"id":"https://openalex.org/keywords/autocorrelation","display_name":"Autocorrelation","score":0.7386859655380249},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6427134871482849},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.6306227445602417},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6027932167053223},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5515282154083252},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5112800598144531},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.47474604845046997},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4230496883392334},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34104931354522705},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12307432293891907},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12015685439109802},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09357234835624695}],"concepts":[{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.9112993478775024},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.900708794593811},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7552546262741089},{"id":"https://openalex.org/C5297727","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation","level":2,"score":0.7386859655380249},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6427134871482849},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.6306227445602417},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6027932167053223},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5515282154083252},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5112800598144531},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.47474604845046997},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4230496883392334},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34104931354522705},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12307432293891907},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12015685439109802},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09357234835624695},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3934/amc.2017030","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2017030","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1304.1984","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.1984","pdf_url":"https://arxiv.org/pdf/1304.1984","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":null},{"id":"mag:1731792027","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1304.1984v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.769.2479","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.769.2479","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1304.1984.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1304.1984","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1304.1984","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/amc.2017030","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2017030","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.47999998927116394}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W1968986695"],"related_works":["https://openalex.org/W2963376294","https://openalex.org/W3093433899","https://openalex.org/W223886575","https://openalex.org/W1977408207","https://openalex.org/W1988571824","https://openalex.org/W3001967807","https://openalex.org/W2383955875","https://openalex.org/W2013878881","https://openalex.org/W1984806471","https://openalex.org/W2562608212","https://openalex.org/W2132391420","https://openalex.org/W3106326766","https://openalex.org/W3084005496","https://openalex.org/W109537178","https://openalex.org/W2055249322","https://openalex.org/W1563766471","https://openalex.org/W2069289311","https://openalex.org/W2101249352","https://openalex.org/W1989359883","https://openalex.org/W1972854678"],"abstract_inverted_index":{"We":[0],"present":[1],"an":[2],"N-dimensional":[3,24],"generalisation":[4],"of":[5,23],"the":[6,21,42],"two-dimensional":[7],"block-circulant":[8],"perfect":[9,38],"array":[10,43],"construction":[11],"by":[12],"Blake":[13,18],"et":[14,19],"al.":[15],"As":[16],"in":[17],"al,":[20],"families":[22],"arrays":[25],"possess":[26],"pairwise":[27],"good":[28],"zero":[29],"correlation":[30],"zone":[31],"(ZCZ)":[32],"cross-correlation.":[33],"Both":[34],"constructions":[35],"use":[36],"a":[37],"autocorrelation":[39],"sequence":[40],"with":[41],"orthogonality":[44],"property":[45],"(AOP).":[46]},"counts_by_year":[],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}