| Issue |
RAIRO-Theor. Inf. Appl.
Volume 58, 2024
Randomness and Combinatorics - Edited by Luca Ferrari & Paolo Massazza
|
|
|---|---|---|
| Article Number | 10 | |
| Number of page(s) | 15 | |
| DOI | https://doi.org/10.1051/ita/2024008 | |
| Published online | 26 March 2024 | |
Finding automatic sequences with few correlations
1
Univ Gustave Eiffel, CNRS, LIGM, F-77454 Marne-la-Vallée, France
2
Univ Rouen Normandie, CNRS, Normandie Univ, LMRS UMR 6085, F-76000 Rouen, France
* Corresponding author: vincent.juge@univ-eiffel.fr
Received:
14
December
2022
Accepted:
23
February
2024
Although automatic sequences are algorithmically very simple, some of them have pseudorandom properties. In particular, some automatic sequences such as the Golay–Shapiro sequence are known to be 2-uncorrelated, meaning that they have the same correlations of order 2 as a uniform random sequence. However, the existence of ℓ-uncorrelated automatic sequences (for ℓ ⩾ 3) was left as an open question in a recent paper of Marcovici, Stoll and Tahay. We exhibit binary block-additive sequences that are 3-uncorrelated and, with the help of analytical results supplemented by an exhaustive search, we present a complete picture of the correlation properties of binary block-additive sequences of rank r ⩽ 5, and ternary sequences of rank r ⩽ 3.
Mathematics Subject Classification: 68R15 / 11B85 / 11K36
Key words: Combinatorics on words / automata sequence / well-distributed sequence
© The authors. Published by EDP Sciences, 2024
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