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Article Dans Une Revue Pure mathematics and applications Année : 2022

Finding automatic sequences with few correlations

Résumé

Although automatic sequences are very simple algorithmically, some of them have pseudo-random 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.
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hal-04323443 , version 1 (15-03-2024)

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Vincent Jugé, Irène Marcovici. Finding automatic sequences with few correlations. Pure mathematics and applications , 2022, 30 (1), pp.75-81. ⟨10.2478/puma-2022-0012⟩. ⟨hal-04323443⟩
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