@inproceedings{cb9aaba30f2c4280a8234515c2a84be2,
title = "Latin Hypercubes and Cellular Automata",
abstract = "Latin squares and hypercubes are combinatorial designs with several applications in statistics, cryptography and coding theory. In this paper, we generalize a construction of Latin squares based on bipermutive cellular automata (CA) to the case of Latin hypercubes of dimension. In particular, we prove that linear bipermutive CA (LBCA) yielding Latin hypercubes of dimension are defined by sequences of invertible Toeplitz matrices with partially overlapping coefficients, which can be described by a specific kind of regular de Bruijn graph induced by the support of the determinant function. Further, we derive the number of k-dimensional Latin hypercubes generated by LBCA by counting the number of paths of length on this de Bruijn graph.",
keywords = "Bipermutivity, Cellular automata, De bruijn graphs, Latin hypercubes, Latin squares, Toeplitz matrices",
author = "Maximilien Gadouleau and Luca Mariot",
year = "2020",
doi = "10.1007/978-3-030-61588-8_11",
language = "English",
isbn = "978-3-030-61587-1",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science+Business Media",
pages = "139--151",
editor = "Hector Zenil",
booktitle = "Cellular Automata and Discrete Complex Systems",
note = "26th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems, AUTOMATA 2020 ; Conference date: 10-08-2020 Through 12-08-2020",
}