  A new construction for constant weight codes is presented. The codes are
constructed from $k$-dimensional subspaces of the vector space $\F_q^n$. These
subspaces form a constant dimension code in the Grassmannian space
$\cG_q(n,k)$. Some of the constructed codes are optimal constant weight codes
with parameters not known before. An efficient algorithm for error-correction
is given for the constructed codes. If the constant dimension code has an
efficient encoding and decoding algorithms then also the constructed constant
weight code has an efficient encoding and decoding algorithms.
