EN|RU Volume 15, No 5, 2008, P. 35-46 UDC 519.174 D. S. Krotov On perfect colorings of the halved 24-cube Abstract: We consider perfect 2-colorings of the distance-2 graph of the 24-cube $\{0,1\}^{24}$ with parameters $((20+c,256-c)(c,276-c))$ (i.e., with the eigenvalue 20). We prove that such colorings exist for all c from 1 to 128 except 1, 2, 4, 5, 7, 10, 13 and do not exist for $c$ = 1, 2, 4, 5, 7.  Tabl. 2, bibl. 4. Keywords: perfect coloring, equitable partition, halved $n$-cube. Krotov Denis Stanislavovich 1 1. S. L. Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia e-mail: krotov@math.nsc.ru © Sobolev Institute of Mathematics, 2015