Codes Associated with Special Linear Groups and Power Moments of Multi-dimensional Kloosterman Sums

摘要

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