co.combinatorics - Indexing schemes of binary sequences

I am looking for "low-complexity" indexing methods to enumerate binary sequences of a given length and a given weight.

Formally, let $T_k^n = {x_1^n in {0,1}^n: sum_{i=1}^n x_i = k}$. How to construct a bijective mapping $f: T_k^n to {1, 2, ldots, binom{n}{k}}$ such that computing each $f(x_1^n)$ needs small number of operations?

For example, one could do lexicographical ordering, that is, e.g., $0110 < 1010$. Then this gives the following scheme:

$f(x_1^n) = sum_{k=1}^n x_k binom{n-k}{w_k}$

where $w_k=sum_{i=k}^n x_i$. Computing $n$ binomial coefficients can be quite demanding. Any other ideas? Or is it impossible to avoid?