{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:35:52Z","timestamp":1740137752297,"version":"3.37.3"},"reference-count":10,"publisher":"EDP Sciences","license":[{"start":{"date-parts":[[2024,3,26]],"date-time":"2024-03-26T00:00:00Z","timestamp":1711411200000},"content-version":"vor","delay-in-days":85,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Theor. Inf. Appl."],"accepted":{"date-parts":[[2024,2,23]]},"published-print":{"date-parts":[[2024]]},"abstract":"<jats:p>Although automatic sequences are algorithmically very simple, some of them have pseudorandom properties. In particular, some automatic sequences such as the Golay\u2013Shapiro 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 \u2113-uncorrelated automatic sequences (for \u2113 \u2a7e 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 <jats:italic>r<\/jats:italic> \u2a7d 5, and ternary sequences of rank <jats:italic>r<\/jats:italic> \u2a7d 3.<\/jats:p>","DOI":"10.1051\/ita\/2024008","type":"journal-article","created":{"date-parts":[[2024,3,26]],"date-time":"2024-03-26T09:11:28Z","timestamp":1711444288000},"page":"10","source":"Crossref","is-referenced-by-count":0,"title":["Finding automatic sequences with few correlations"],"prefix":"10.1051","volume":"58","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0834-9082","authenticated-orcid":false,"given":"Vincent","family":"Jug\u00e9","sequence":"first","affiliation":[]},{"given":"Ir\u00e8ne","family":"Marcovici","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2024,3,26]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Allouche J.-P. and Shallit J., Automatic sequences. Theory, Applications, Generalizations. Cambridge University Press, Cambridge (2003).","key":"R1","DOI":"10.1017\/CBO9780511546563"},{"key":"R2","doi-asserted-by":"crossref","first-page":"345","DOI":"10.4064\/aa140-4-5","volume":"140","author":"Grant","year":"2009","journal-title":"Acta Arith."},{"unstructured":"Marcovici I., Stoll T. and Tahay P.-A., Discrete correlations of order 2 of generalized Golay\u2014Shapiro sequences: a combinatorial approach. Integers 21 (2021) #A45.","key":"R3"},{"key":"R4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2478\/udt-2020-0001","volume":"15","author":"Tahay","year":"2020","journal-title":"Unif. Distrib. Theory"},{"key":"R5","doi-asserted-by":"crossref","first-page":"299","DOI":"10.4064\/aa135-4-1","volume":"135","author":"Drmota","year":"2008","journal-title":"Acta Arith."},{"key":"R6","doi-asserted-by":"crossref","first-page":"1096","DOI":"10.4153\/CJM-2017-053-1","volume":"70","author":"M\u00fcllner","year":"2018","journal-title":"Canad. J. Math."},{"unstructured":"Cateland E., Digital Sequences and k-regular Sequences. Theses, \u00dcniversite Sciences et Technologies \u2014 Bordeaux I (1992).","key":"R7"},{"key":"R8","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1515\/udt-2016-0021","volume":"11","author":"Allouche","year":"2016","journal-title":"Unif. Distrib. Theory"},{"key":"R9","doi-asserted-by":"crossref","first-page":"115","DOI":"10.5802\/aif.1089","volume":"37","author":"Queff\u00e9lec","year":"1987","journal-title":"Ann. Inst. Fourier (Grenoble)"},{"unstructured":"Juge V., Detecting correlations in automatic sequences, (2024), 1, 10.5281\/zenodo.10792181","key":"R10"}],"container-title":["RAIRO - Theoretical Informatics and Applications"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ita.org\/10.1051\/ita\/2024008\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,26]],"date-time":"2024-03-26T09:11:40Z","timestamp":1711444300000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ita.org\/10.1051\/ita\/2024008"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"references-count":10,"alternative-id":["ita220054"],"URL":"https:\/\/doi.org\/10.1051\/ita\/2024008","relation":{},"ISSN":["0988-3754","2804-7346"],"issn-type":[{"type":"print","value":"0988-3754"},{"type":"electronic","value":"2804-7346"}],"subject":[],"published":{"date-parts":[[2024]]}}}