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

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dc.creatorKim, Dae San
dc.date2008-07-25
dc.date.accessioned2026-07-07T09:52:49Z
dc.date.available2026-07-07T09:52:49Z
dc.descriptionIn 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.
dc.identifierhttps://arxiv.org/abs/0807.3991
dc.identifierhttp://arxiv.org/abs/0807.3991
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/165733
dc.subjectNumber Theory
dc.subjectInformation Theory
dc.subject11T23; 20G40; 94B05
dc.titleCodes Associated with Special Linear Groups and Power Moments of Multi-dimensional Kloosterman Sums
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