  We construct perfect $2$-colorings of the $12$-hypercube that attain our
recent bound on the dimension of arbitrary correlation immune functions. We
prove that such colorings with parameters $(x,12-x,4+x,8-x$) exist if $x=0$,
$2$, $3$ and do not exist if $x=1$.
  This is a translation into English of the original paper by D. G.
Fon-Der-Flaass, "Perfect colorings of the $12$-cube that attain the bound on
correlation immunity", published in Russian in Siberian Electronic Mathematical
Reports, vol. 4 (2007) 292-295.
