{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:46:56Z","timestamp":1760240816069,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2019,9,24]],"date-time":"2019-09-24T00:00:00Z","timestamp":1569283200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JP16K06361","JP19K12158"],"award-info":[{"award-number":["JP16K06361","JP19K12158"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The statistical properties of chaotic binary sequences generated by the Bernoulli map and Walsh functions are discussed. The Walsh functions are based on a      2 k  \u00d7  2 k      Hadamard matrix. For general k (=    1 , 2 , \u22ef    ), we will prove that     2  k - 1      Walsh functions can generate essentially different balanced and i.i.d. binary sequences that are orthogonal to each other.<\/jats:p>","DOI":"10.3390\/e21100930","type":"journal-article","created":{"date-parts":[[2019,9,25]],"date-time":"2019-09-25T03:51:18Z","timestamp":1569383478000},"page":"930","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Orthogonal Chaotic Binary Sequences Based on Bernoulli Map and Walsh Functions"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6531-2043","authenticated-orcid":false,"given":"Akio","family":"Tsuneda","sequence":"first","affiliation":[{"name":"Division of Informatics and Energy, Faculty of Advanced Science and Technology, Kumamoto University, Kumaomto 860-8555, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1109\/18.567654","article-title":"Statistics of chaotic binary sequences","volume":"43","author":"Kohda","year":"1997","journal-title":"IEEE Trans. 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