On the maximal autocorrelation of Rudin-Shapiro sequences
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In this paper, we prove that the maximal aperiodic autocorrelation of the m-th Rudin-Shapiro sequence is of the same order as λ^m, where λ is the real root of x^3 + x^2 - 2x - 4. This proof was developed independently of the recently published proof given by Katz and van der Linden (2021). A proof of this result for the related periodic autocorrelation is given by Allouche, Choi, Denise, Erdélyi, and Saffari (2019) and Choi (2020) using a translation of the problem into linear algebra. Our approach modifies this linear algebraic translation to deal with aperiodic autocorrelation and provides an alternative method of dealing with the computations given by Choi.
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