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Orthogonal Chaotic Binary Sequences Based on Bernoulli Map and Walsh Functions

Division of Informatics and Energy, Faculty of Advanced Science and Technology, Kumamoto University, Kumaomto 860-8555, Japan
Entropy 2019, 21(10), 930; https://doi.org/10.3390/e21100930
Received: 30 August 2019 / Revised: 19 September 2019 / Accepted: 23 September 2019 / Published: 24 September 2019
(This article belongs to the Section Information Theory, Probability and Statistics)
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 × 2 k Hadamard matrix. For general k (= 1 , 2 , ), 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. View Full-Text
Keywords: Bernoulli map; orthogonal sequence; Walsh functions; chaotic binary sequence; correlation property; i.i.d. Bernoulli map; orthogonal sequence; Walsh functions; chaotic binary sequence; correlation property; i.i.d.
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Tsuneda, A. Orthogonal Chaotic Binary Sequences Based on Bernoulli Map and Walsh Functions. Entropy 2019, 21, 930.

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