On transversals of splitted Latin squares with identical substitution ${\chi_{ACDB}}$

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.