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

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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. 
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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/