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Codes Associated with and Power Moments of Kloosterman Sums
-
Dae San Kim
Published/Copyright:
March 27, 2012
Abstract.
We shall construct three binary linear codes
, 
, and 
, respectively
associated with the orthogonal groups 
, 
, and
, with 
a power of two. Then we obtain recursive
formulas for the power moments of Kloosterman and 2-dimensional
Kloosterman sums in terms of the frequencies of weights in the
codes. This is done via the Pless power moment identity and by utilizing
the explicit expressions of Gauss sums for the orthogonal groups.
Keywords.: Kloosterman Sum; Orthogonal Group; Pless Power Moment Identity; Weight Distribution; Gauss Sum
Received: 2010-08-30
Accepted: 2011-09-19
Published Online: 2012-03-27
Published in Print: 2012-April
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
Kloosterman Sum;
Orthogonal Group;
Pless Power Moment Identity;
Weight Distribution;
Gauss Sum
Articles in the same Issue
- Masthead
- Odd Catalan Numbers Modulo
- Variations of the Poincaré Map
- Diophantine Equations of Matching Games I
- Norm Euclidean Quaternionic Orders
- A New Proof of Winquist's Identity
- Counting Depth Zero Patterns in Ballot Paths
- Codes Associated with and Power Moments of Kloosterman Sums
- Subprime Factorization and the Numbers of Binomial Coefficients Exactly Divided by Powers of a Prime
- Generalized Nonaveraging Integer Sequences
- The Robin Inequality for 7-Free Integers
- On 3-adic Valuations of Generalized Harmonic Numbers
