Kloosterman sum identities and low-weight codewords in a cyclic code with two zeros

Authors:
Marko Moisio;Kalle Ranto
Affiliations:
Department of Mathematics and Statistics, University of Vaasa, PO Box 700, FIN-65101 Vaasa, Finland;Department of Mathematics, University of Turku, FIN-20014 Turku, Finland
Venue:
Finite Fields and Their Applications
Year:
2007

Citing 5
Cited 3

Hecke operators and the weight distributions of certain codes

Journal of Combinatorial Theory Series A
Finite fields

Finite fields
The weights of the orthogonals of the extended quadratic binary Goppa codes

IEEE Transactions on Information Theory
Propagation characteristics of x→ x-1 and Kloosterman sums

Finite Fields and Their Applications
On the number of rational points on some families of Fermat curves over finite fields

Finite Fields and Their Applications

On the Connection between Kloosterman Sums and Elliptic Curves

SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
On the values of Kloosterman sums

IEEE Transactions on Information Theory
On ternary Kloosterman sums modulo 12

Finite Fields and Their Applications

Quantified Score

Hi-index	0.06

Visualization

Abstract

We apply relations of n-dimensional Kloosterman sums to exponential sums over finite fields to count the number of low-weight codewords in a cyclic code with two zeros. As a corollary we obtain a new proof for a result of Carlitz which relates one- and two-dimensional Kloosterman sums. In addition, we count some power sums of Kloosterman sums over certain subfields.