Orthogonal Chaotic Binary Sequences Based on Bernoulli Map and Walsh Functions - Akio Tsuneda (Entropy, 2019)
The statistical properties of chaotic binary sequences generated by the Bernoulli map and Walsh functions are discussed. The Walsh functions are based on a <semantics> 2 k × 2 k </semantics> Hadamard matrix. For general k (= <semantics> 1 , 2 , ⋯ </semantics> ), we will prove that <semantics> 2 k - 1 </semantics> Walsh functions can generate essentially different balanced and i.i.d. binary sequences that are orthogonal to each other.