Geodesic
Recursive formulas generating power moments of multi-dimensional Kloosterman sums and $m$-multiple power moments of Kloosterman sums
Algebra and discrete mathematics, Tome 19 (2015) no. 2, pp. 213-228

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we construct two binary linear codes associated with multi-dimensional and $m -$multiple power Kloosterman sums (for any fixed $m$) over the finite field $\mathbb{F}_{q}$. Here $q$ is a power of two. The former codes are dual to a subcode of the binary hyper-Kloosterman code. Then we obtain two recursive formulas for the power moments of multi-dimensional Kloosterman sums and for the $m$-multiple power moments of Kloosterman sums in terms of the frequencies of weights in the respective codes. This is done via Pless power moment identity and yields, in the case of power moments of multi-dimensional Kloosterman sums, much simpler recursive formulas than those associated with finite special linear groups obtained previously.
Keywords: index terms-recursive formula, multi-dimensional Kloosterman sum, Kloosterman sum, Pless power moment identity, weight distribution. 
@article{ADM_2015_19_2_a5,
     author = {Dae San Kim},
     title = {Recursive formulas generating power moments of multi-dimensional {Kloosterman} sums and $m$-multiple power moments of {Kloosterman} sums},
     journal = {Algebra and discrete mathematics},
     pages = {213--228},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2015_19_2_a5/}
}
TY  - JOUR
AU  - Dae San Kim
TI  - Recursive formulas generating power moments of multi-dimensional Kloosterman sums and $m$-multiple power moments of Kloosterman sums
JO  - Algebra and discrete mathematics
PY  - 2015
SP  - 213
EP  - 228
VL  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2015_19_2_a5/
LA  - en
ID  - ADM_2015_19_2_a5
ER  - 
%0 Journal Article
%A Dae San Kim
%T Recursive formulas generating power moments of multi-dimensional Kloosterman sums and $m$-multiple power moments of Kloosterman sums
%J Algebra and discrete mathematics
%D 2015
%P 213-228
%V 19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2015_19_2_a5/
%G en
%F ADM_2015_19_2_a5
Dae San Kim. Recursive formulas generating power moments of multi-dimensional Kloosterman sums and $m$-multiple power moments of Kloosterman sums. Algebra and discrete mathematics, Tome 19 (2015) no. 2, pp. 213-228. http://geodesic.mathdoc.fr/item/ADM_2015_19_2_a5/