Recursive formulas generating power moments of multi-dimensional Kloosterman sums and $m$-multiple power moments of Kloosterman sums

Details Recursive formulas generating power moments of multi-dimensional Kloosterman sums and $m$-multiple power moments of Kloosterman sums Recursive formulas generating power moments of multi-dimensional Kloosterman sums and $m$-multiple power moments of Kloosterman sums

2009-09-07

arxiv.org/abs/0909.1153v1

Mathematics

Number Theory

14 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Recursive formulas generating power moments of multi-dimensional Kloosterman sums and $m$-multiple power moments of Kloosterman sums does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Recursive formulas generating power moments of multi-dimensional Kloosterman sums and $m$-multiple power moments of Kloosterman sums, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Recursive formulas generating power moments of multi-dimensional Kloosterman sums and $m$-multiple power moments of Kloosterman sums will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-295254