On finite pseudorandom binary sequences. II: The Champernowne, Rudin-Shapiro, and Thue-Morse sequences, a further construction

DOI10.1006/jnth.1998.2286zbMath0916.11047OpenAlexW1979902210MaRDI QIDQ1277184

Christian Mauduit, András Sárközy

Publication date: 2 February 1999

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1998.2286

zbMATH Keywords

Thue-Morse sequencesmeasures of pseudorandomnessbinary alphabetspecial sequenceswell-distributionRudin-Shapiro sequencesChampernowne sequencessmall correlationtests for pseudorandomness

Mathematics Subject Classification ID

Special sequences and polynomials (11B83) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (29)

Sums of digits of multiples of integers ⋮ Maximum order complexity of the sum of digits function in Zeckendorf base and polynomial subsequences ⋮ On the maximum order complexity of Thue-Morse and Rudin-Shapiro sequences along polynomial values ⋮ On finite pseudorandom sequences of \(k\) symbols ⋮ GOWERS UNIFORMITY NORM AND PSEUDORANDOM MEASURES OF THE PSEUDORANDOM BINARY SEQUENCES ⋮ Generalized Hausdorff dimensions of sets of real numbers with zero entropy expansion ⋮ On the correlation of families of pseudorandom sequences of $k$ symbols ⋮ Pseudorandom sequences derived from automatic sequences ⋮ An algorithm for the word entropy ⋮ Automatic sequences as good weights for ergodic theorems ⋮ On the pseudorandomness of automatic sequences ⋮ Algorithmic classification of noncorrelated binary pattern sequences ⋮ q-ADDITIVE FUNCTIONS ON POLYNOMIAL SEQUENCES ⋮ Pseudorandom number generation using chaotic true orbits of the Bernoulli map ⋮ The truncated sum-of-digits function of powers ⋮ On the correlation measures of subsets ⋮ On the measures of pseudorandomness of binary sequences. ⋮ On the \(N\)th maximum order complexity and the expansion complexity of a Rudin-Shapiro-like sequence ⋮ Subsequences of automatic sequences indexed by \(\lfloor n^c \rfloor\) and correlations ⋮ More constructions of pseudorandom sequences of \(k\) symbols ⋮ On the \(N\)th linear complexity of automatic sequences ⋮ Construction of large families of pseudorandom binary sequences ⋮ Champernowne’s Number, Strong Normality, and the X Chromosome ⋮ On pseudo-random subsets of \({\mathbb{Z}}_n\) ⋮ Complexity and fractal dimensions for infinite sequences with positive entropy ⋮ Spectral properties of pattern sequences of general degrees ⋮ Gowers norms for the Thue-Morse and Rudin-Shapiro sequences ⋮ Finite and infinite pseudorandom binary words ⋮ On finite pseudorandom sequences of \(k\) symbols.

Cites Work

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• Substitution dynamical systems - spectral analysis
• Sums of digits and almost primes
• Some Theorems on Fourier Coefficients
• The number of factors in a paperfolding sequence
• On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol
• The Construction of Decimals Normal in the Scale of Ten
• Sur les nombres qui ont des propriétés additives et multiplicatives données

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