Geodesic
On transversals of splitted Latin squares with identical substitution ${\chi_{ACDB}}$
Matematičeskie voprosy kriptografii, Tome 11 (2020) no. 1, pp. 9-26 
V. V. Borisenko. On transversals of splitted Latin squares with identical substitution ${\chi_{ACDB}}$. Matematičeskie voprosy kriptografii, Tome 11 (2020) no. 1, pp. 9-26. http://geodesic.mathdoc.fr/item/MVK_2020_11_1_a1/
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     author = {V. V. Borisenko},
     title = {On transversals of splitted {Latin} squares with identical substitution ${\chi_{ACDB}}$},
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     url = {http://geodesic.mathdoc.fr/item/MVK_2020_11_1_a1/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the splitted homogeneous Latin squares, i.e. Latin squares of order $2n$ with elements from $\left\{0, \ldots, 2n - 1\right\}$ such that reducing modulo $n$ leads to a $\left( 2n \times 2n \right)$-matrix consisting of four Latin squares $\left(A,B,C,D\right)$ of order $n$ with identity $\chi_{ACDB}$ permutation. The method for finding all possible numbers of transversals for Latin Squares of this kind of order $2n$ was described. This method is based on the notion of transversal code introduced in the paper.

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