Geodesic
$k$-homogeneous Latin Squares, their transversals and condition of pseudo-orthogonality
Matematičeskie voprosy kriptografii, Tome 14 (2023) no. 3, pp. 75-84 Cet article a éte moissonné depuis la source Math-Net.Ru

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We describe a method for transforming any system of $t$ mutually orthogonal Latin squares into a system of $t$ mutually pseudo-orthogonal Latin squares. We consider the $k$-homogeneous Latin Squares, i.e. Latin Squares of order $kn$ with elements from ${0,\dots,kn-1}$ such that after reducing modulo $n$ we obtain $(kn\times kn)$-matrix consisting of $k^2$ identical Latin Squares of order $n$. Some characteristics of transversals of $k$-homogeneous Latin Squares are described. Sufficient condition of pseudo-orthogonality is presented. 
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V. V. Borisenko. $k$-homogeneous Latin Squares, their transversals and condition of pseudo-orthogonality. Matematičeskie voprosy kriptografii, Tome 14 (2023) no. 3, pp. 75-84. http://geodesic.mathdoc.fr/item/MVK_2023_14_3_a4/

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