  Codes in the Grassmannian space have found recently application in network
coding. Representation of $k$-dimensional subspaces of $\F_q^n$ has generally
an essential role in solving coding problems in the Grassmannian, and in
particular in encoding subspaces of the Grassmannian. Different representations
of subspaces in the Grassmannian are presented. We use two of these
representations for enumerative encoding of the Grassmannian. One enumerative
encoding is based on Ferrers diagrams representation of subspaces; and another
is based on identifying vector and reduced row echelon form representation of
subspaces. A third method which combine the previous two is more efficient than
the other two enumerative encodings.
