{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T15:28:39Z","timestamp":1780500519949,"version":"3.54.1"},"reference-count":18,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,9,30]],"date-time":"2021-09-30T00:00:00Z","timestamp":1632960000000},"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":["JP19K12158"],"award-info":[{"award-number":["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>This paper discusses the auto-correlation functions of m-bit random numbers obtained from m chaotic binary sequences generated by one-dimensional nonlinear maps. First, we provide the theoretical auto-correlation function of an m-bit sequence obtained by m binary sequences that are assumed to be uncorrelated to each other. The auto-correlation function is expressed by a simple form using the auto-correlation functions of the binary sequences. This implies that the auto-correlation properties of the m-bit sequences can be easily controlled by the auto-correlation functions of the original binary sequences. In numerical experiments using a computer, we generated m-bit random sequences using some chaotic binary sequences with prescribed auto-correlations generated by one-dimensional chaotic maps. The numerical experiments show that the numerical auto-correlation values are almost equal to the corresponding theoretical ones, and we can generate m-bit sequences with a variety of auto-correlation properties. Furthermore, we also show that the distributions of the generated m-bit sequences are uniform if all of the original binary sequences are balanced (i.e., the probability of 1 (or 0) is equal to 1\/2) and independent of one another.<\/jats:p>","DOI":"10.3390\/e23101295","type":"journal-article","created":{"date-parts":[[2021,10,1]],"date-time":"2021-10-01T10:55:40Z","timestamp":1633085740000},"page":"1295","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Various Auto-Correlation Functions of m-Bit Random Numbers Generated from Chaotic Binary Sequences"],"prefix":"10.3390","volume":"23","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, Kumamoto 860-8555, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,30]]},"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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