Geodesic
Constant weight perfect and $D$-representable codes
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2012), pp. 16-19.

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

The problem of the existence of non trivial constant weight perfect codes in the $B^n$-space defined over $GF(2)$ remains unsolved up to now. It has been proved in the present paper that the problem of the existence of constant weight perfect codes is equivalent to the problem of the existence of $D$-representable codes in the fixed layer.
Keywords: constant weight perfect codes, space splitting, Dirichlet regions, $D$-representable codes. 
@article{UZERU_2012_1_a2,
     author = {V. K. Leont'ev and G. L. Movsisyan and Zh. G. Margaryan},
     title = {Constant weight perfect and $D$-representable codes},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {16--19},
     publisher = {mathdoc},
     number = {1},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2012_1_a2/}
}
TY  - JOUR
AU  - V. K. Leont'ev
AU  - G. L. Movsisyan
AU  - Zh. G. Margaryan
TI  - Constant weight perfect and $D$-representable codes
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2012
SP  - 16
EP  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2012_1_a2/
LA  - en
ID  - UZERU_2012_1_a2
ER  - 
%0 Journal Article
%A V. K. Leont'ev
%A G. L. Movsisyan
%A Zh. G. Margaryan
%T Constant weight perfect and $D$-representable codes
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2012
%P 16-19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2012_1_a2/
%G en
%F UZERU_2012_1_a2
V. K. Leont'ev; G. L. Movsisyan; Zh. G. Margaryan. Constant weight perfect and $D$-representable codes. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2012), pp. 16-19. http://geodesic.mathdoc.fr/item/UZERU_2012_1_a2/

[1] V. A. Zinov'ev, V. K. Leont'ev, “On Non-Existence of Perfect Codes in Error Correcting Codes”, Problems of Control and Inform. Theory, 2:2 (1973), 123–132 (in Russian) | MR | Zbl

[2] A. Tiettavainen, “On the Nonexistence of Perfect Codes over Finite Fields”, SIAM J. Appl. Math., 24 (1973), 88–96 | DOI | MR

[3] G. L. Movsisyan, Zh. G. Margaryan, “D-Representing Code Problem Solution”, Fundamentals of Computation Theory, International Conference FCT 87 (USSR, Kazan, 1987), 328–331

[4] P. Delsarte, “An Algebraic Approach to the Association Schemes of Coding Theory”, Philips Research Reports Supplements, 1973, no. 10, 97 | MR | Zbl

[5] G. L. Movsisyan, “Perfect codes in Johnson schemes.”, Bulletin of MSU, Computing Math. and Cybernetics, 1:15 (1982), 64–69 (in Russian) | MR | Zbl