{"id":"https://openalex.org/W2977238808","doi":"https://doi.org/10.3390/e21100930","title":"Orthogonal Chaotic Binary Sequences Based on Bernoulli Map and Walsh Functions","display_name":"Orthogonal Chaotic Binary Sequences Based on Bernoulli Map and Walsh Functions","publication_year":2019,"publication_date":"2019-09-24","ids":{"openalex":"https://openalex.org/W2977238808","doi":"https://doi.org/10.3390/e21100930","mag":"2977238808"},"language":"en","primary_location":{"id":"doi:10.3390/e21100930","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21100930","pdf_url":"https://www.mdpi.com/1099-4300/21/10/930/pdf?version=1570333812","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/21/10/930/pdf?version=1570333812","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015351071","display_name":"Akio Tsuneda","orcid":"https://orcid.org/0000-0002-6531-2043"},"institutions":[{"id":"https://openalex.org/I96036126","display_name":"Kumamoto University","ror":"https://ror.org/02cgss904","country_code":"JP","type":"education","lineage":["https://openalex.org/I96036126"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Akio Tsuneda","raw_affiliation_strings":["Division of Informatics and Energy, Faculty of Advanced Science and Technology, Kumamoto University, Kumaomto 860-8555, Japan"],"raw_orcid":"https://orcid.org/0000-0002-6531-2043","affiliations":[{"raw_affiliation_string":"Division of Informatics and Energy, Faculty of Advanced Science and Technology, Kumamoto University, Kumaomto 860-8555, Japan","institution_ids":["https://openalex.org/I96036126"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015351071"],"corresponding_institution_ids":["https://openalex.org/I96036126"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.3692,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.5672125,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"21","issue":"10","first_page":"930","last_page":"930"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11130","display_name":"Coding theory and cryptography","score":0.994700014591217,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/walsh-function","display_name":"Walsh function","score":0.8420807123184204},{"id":"https://openalex.org/keywords/bernoullis-principle","display_name":"Bernoulli's principle","score":0.8184491395950317},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.8003889322280884},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.7026685476303101},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.650825560092926},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6352398991584778},{"id":"https://openalex.org/keywords/hadamard-matrix","display_name":"Hadamard matrix","score":0.5686310529708862},{"id":"https://openalex.org/keywords/orthogonal-functions","display_name":"Orthogonal functions","score":0.49482887983322144},{"id":"https://openalex.org/keywords/orthogonal-matrix","display_name":"Orthogonal matrix","score":0.44662410020828247},{"id":"https://openalex.org/keywords/bernoulli-scheme","display_name":"Bernoulli scheme","score":0.4421892762184143},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38676750659942627},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36226367950439453},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34004226326942444},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20161527395248413},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16966772079467773},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16034367680549622},{"id":"https://openalex.org/keywords/orthogonal-basis","display_name":"Orthogonal basis","score":0.1376672089099884},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10680344700813293},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.091339111328125}],"concepts":[{"id":"https://openalex.org/C164319782","wikidata":"https://www.wikidata.org/wiki/Q1934233","display_name":"Walsh function","level":2,"score":0.8420807123184204},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.8184491395950317},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.8003889322280884},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.7026685476303101},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.650825560092926},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6352398991584778},{"id":"https://openalex.org/C30463267","wikidata":"https://www.wikidata.org/wiki/Q1422682","display_name":"Hadamard matrix","level":3,"score":0.5686310529708862},{"id":"https://openalex.org/C135925592","wikidata":"https://www.wikidata.org/wiki/Q2637908","display_name":"Orthogonal functions","level":2,"score":0.49482887983322144},{"id":"https://openalex.org/C44292817","wikidata":"https://www.wikidata.org/wiki/Q333871","display_name":"Orthogonal matrix","level":3,"score":0.44662410020828247},{"id":"https://openalex.org/C164528419","wikidata":"https://www.wikidata.org/wiki/Q3042439","display_name":"Bernoulli scheme","level":3,"score":0.4421892762184143},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38676750659942627},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36226367950439453},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34004226326942444},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20161527395248413},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16966772079467773},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16034367680549622},{"id":"https://openalex.org/C187064257","wikidata":"https://www.wikidata.org/wiki/Q3306808","display_name":"Orthogonal basis","level":2,"score":0.1376672089099884},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10680344700813293},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.091339111328125},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e21100930","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21100930","pdf_url":"https://www.mdpi.com/1099-4300/21/10/930/pdf?version=1570333812","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:pubmedcentral.nih.gov:7514262","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7514262","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:f38e7e40feb943ecab4d50c87f8166c7","is_oa":true,"landing_page_url":"https://doaj.org/article/f38e7e40feb943ecab4d50c87f8166c7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 21, Iss 10, p 930 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/21/10/930/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e21100930","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e21100930","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21100930","pdf_url":"https://www.mdpi.com/1099-4300/21/10/930/pdf?version=1570333812","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3667028330","display_name":"Fundamental Study on Random Techniques Using Chaos Theory","funder_award_id":"19K12158","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5064411550","display_name":"Code Design Based on Chaos Theory and Its Application to Short-Range Communication","funder_award_id":"16K06361","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W86370709","https://openalex.org/W1503108228","https://openalex.org/W1561991101","https://openalex.org/W1913313886","https://openalex.org/W1954740779","https://openalex.org/W1968971721","https://openalex.org/W1985133056","https://openalex.org/W2081024858","https://openalex.org/W2102875151","https://openalex.org/W2117095095","https://openalex.org/W2160851513","https://openalex.org/W2165130379","https://openalex.org/W2482944896","https://openalex.org/W2725458275","https://openalex.org/W2890103732","https://openalex.org/W2904214469","https://openalex.org/W2905420870","https://openalex.org/W3099556301","https://openalex.org/W4285719527","https://openalex.org/W6630203834","https://openalex.org/W6683647496"],"related_works":["https://openalex.org/W2483440357","https://openalex.org/W2088413367","https://openalex.org/W2141437629","https://openalex.org/W2084313316","https://openalex.org/W2142284114","https://openalex.org/W2186692800","https://openalex.org/W2097505662","https://openalex.org/W2977238808","https://openalex.org/W4390048326","https://openalex.org/W2097680982"],"abstract_inverted_index":{"The":[0,17],"statistical":[1],"properties":[2],"of":[3],"chaotic":[4],"binary":[5,58],"sequences":[6,59],"generated":[7],"by":[8],"the":[9],"Bernoulli":[10],"map":[11],"and":[12,56],"Walsh":[13,18,49],"functions":[14,19,50],"are":[15,20,61],"discussed.":[16],"based":[21],"on":[22],"a":[23],"2":[24,27,37,45],"k":[25,28,33,46],"\u00d7":[26],"Hadamard":[29],"matrix.":[30],"For":[31],"general":[32],"(=":[34],"1":[35,48],",":[36,38],"\u22ef":[39],"),":[40],"we":[41],"will":[42],"prove":[43],"that":[44,60],"-":[47],"can":[51],"generate":[52],"essentially":[53],"different":[54],"balanced":[55],"i.i.d.":[57],"orthogonal":[62],"to":[63],"each":[64],"other.":[65]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}
