Geodesic
On transversals of homogeneous Latin squares
Matematičeskie voprosy kriptografii, Tome 6 (2015) no. 3, pp. 5-17 
V. V. Borisenko. On transversals of homogeneous Latin squares. Matematičeskie voprosy kriptografii, Tome 6 (2015) no. 3, pp. 5-17. http://geodesic.mathdoc.fr/item/MVK_2015_6_3_a0/
@article{MVK_2015_6_3_a0,
     author = {V. V. Borisenko},
     title = {On transversals of homogeneous {Latin} squares},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {5--17},
     year = {2015},
     volume = {6},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2015_6_3_a0/}
}
TY  - JOUR
AU  - V. V. Borisenko
TI  - On transversals of homogeneous Latin squares
JO  - Matematičeskie voprosy kriptografii
PY  - 2015
SP  - 5
EP  - 17
VL  - 6
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MVK_2015_6_3_a0/
LA  - ru
ID  - MVK_2015_6_3_a0
ER  - 
%0 Journal Article
%A V. V. Borisenko
%T On transversals of homogeneous Latin squares
%J Matematičeskie voprosy kriptografii
%D 2015
%P 5-17
%V 6
%N 3
%U http://geodesic.mathdoc.fr/item/MVK_2015_6_3_a0/
%G ru
%F MVK_2015_6_3_a0

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider homogeneous Latin squares, i.e. Latin squares of order $2n$ with elements from $\{0,\dots,2n-1\}$ such that after reducing modulo $n$ we obtain $2n\times2n$-matrix consisting of four identical Latin squares of order $n$. The set of all transversals of homogeneous Latin squares is described in a general case; homogeneous Latin squares of order 10 are considered in more detail.

[1] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, MTsNMO, M., 2004

[2] C. J. Colbourn, J. H. Dinitzm (eds.), Handbook of combinatorial designs, 2nd ed., Chapman Hall/CRC Press, 2006 | MR

[3] Borisenko V. V., “O transversalyakh raspavshikhsya latinskikh kvadratov chetnogo poryadka”, Matematicheskie voprosy kriptografii, 5:1 (2014), 5–25