  In this paper, we construct the binary linear codes $C(SL(n,q))$ associated
with finite special linear groups $SL(n,q)$, with both \emph{n,q} powers of
two. Then, via Pless power moment identity and utilizing our previous result on
the explicit expression of the Gauss sum for $SL(n,q)$, we obtain a recursive
formula for the power moments of multi-dimensional Kloosterman sums in terms of
the frequencies of weights in $C(SL(n,q))$. In particular, when $n=2$, this
gives a recursive formula for the power moments of Kloosterman sums. We
illustrate our results with some examples.
