Pseudogeometries with clusters and an example of a~recursive $[4,2,3]_{42}$-code
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 4, pp. 181-192.

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

In 1998, E. Couselo, S. Gonzalez, V. Markov, and A. Nechaev defined the recursive codes and obtained some results that allowed one to conjecture the existence of recursive MDS-codes of dimension 2 and length 4 over any finite alphabet of cardinality $q\notin\{2,6\}$. This conjecture remained open only for $q\in\{14,18,26,42\}$. It is shown in this paper that there exist such codes for $q=42$. We used a new construction, that of pseudogeometry with clusters.
@article{FPM_2008_14_4_a11,
     author = {V. T. Markov and A. A. Nechaev and S. Skazhenik and E. O. Tveritinov},
     title = {Pseudogeometries with clusters and an example of a~recursive $[4,2,3]_{42}$-code},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {181--192},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a11/}
}
TY  - JOUR
AU  - V. T. Markov
AU  - A. A. Nechaev
AU  - S. Skazhenik
AU  - E. O. Tveritinov
TI  - Pseudogeometries with clusters and an example of a~recursive $[4,2,3]_{42}$-code
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2008
SP  - 181
EP  - 192
VL  - 14
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a11/
LA  - ru
ID  - FPM_2008_14_4_a11
ER  - 
%0 Journal Article
%A V. T. Markov
%A A. A. Nechaev
%A S. Skazhenik
%A E. O. Tveritinov
%T Pseudogeometries with clusters and an example of a~recursive $[4,2,3]_{42}$-code
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2008
%P 181-192
%V 14
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a11/
%G ru
%F FPM_2008_14_4_a11
V. T. Markov; A. A. Nechaev; S. Skazhenik; E. O. Tveritinov. Pseudogeometries with clusters and an example of a~recursive $[4,2,3]_{42}$-code. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 4, pp. 181-192. http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a11/

[1] Gonsales S., Kouselo E., Markov V. T., Nechaev A. A., “Rekursivnye MDR-kody i rekursivno differentsiruemye kvazigruppy”, Diskret. mat., 10:2 (1998), 3–29 | MR | Zbl

[2] Gonsales S., Kouselo E., Markov V., Nechaev A., “Parametry rekursivnykh MDR-kodov”, Diskret. mat., 12:4 (2000), 3–24 | MR | Zbl

[3] MakVilyams F. Dzh., Sloen N. Dzh. A., Teoriya kodov, ispravlyayuschikh oshibki, Svyaz, M., 1979

[4] Kholl M., Kombinatorika, Mir, M., 1970 | MR

[5] Tarry G., “Le problème de 36 officiers. 1”, C. R. Assoc. Fr. Av. Sci., 1900, 122–123; “Le problème de 36 officiers. 2”, 1901, 170–203