2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165733In 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.Number TheoryInformation Theory11T23; 20G40; 94B05text