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On finite pseudorandom binary sequences. II: The Champernowne, Rudin-Shapiro, and Thue-Morse sequences, a further construction. (English) Zbl 0916.11047
This interesting paper is the continuation of part I, which appeared in Acta Arith. 82, 365-377 (1997; Zbl 0886.11048). The authors consider special sequences over a binary alphabet and present some arithmetic tests for pseudorandomness. As measures of pseudorandomness, well-distribution relative to arithmetic progressions and small (auto) correlation are used. These properties of the Champernowne, the Thue-Morse and the Rudin-Shapiro sequences are studied, and it is shown that these sequences are not sufficiently well distributed to be considered as pseudorandom. Finally, by using the Legendre symbol and permutation polynomials, a nearly ideally pseudorandom sequence is constructed. The proof of this result heavily depends on character sum estimates.
Reviewer: R.F.Tichy (Graz)

MSC:
11K45 Pseudo-random numbers; Monte Carlo methods
11B83 Special sequences and polynomials
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