Abstract
As a generalization of perpendicular arrays defined by C. R. Rao in 1961, Li et al. have newly introduced a combinatorial array, called a perpendicular multi-array, in 2018 for constructions of splitting authentication codes having some perfect t-fold secrecy. Moreover, several classes of perpendicular multi-arrays have been constructed in the literature. In this paper, necessary conditions for the existence of a perpendicular multi-array are discussed, and fundamental/useful results for the existence of perpendicular multi-arrays are provided by use of the results on combinatorial designs. As a main result, it is shown that the necessary conditions are also sufficient for the existence of a perpendicular multi-array with block size \(3\times 2\) with the only one exception. Finally, the asymptotic existence of perpendicular multi-arrays with a cyclic automorphism is presented.
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Matsubara, K., Kageyama, S. (2021). The Existence of Perpendicular Multi-arrays. In: Arnold, B.C., Balakrishnan, N., Coelho, C.A. (eds) Methodology and Applications of Statistics. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-83670-2_13
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