On a new identity for Kloosterman sums and nonlinear system of equations over finite fields of characteristic 2.

DOI10.1016/S0012-365X(03)00083-9zbMath1048.11096OpenAlexW1970554159MaRDI QIDQ1421515

Victor A. Zinoviev, Tor Helleseth

Publication date: 26 January 2004

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0012-365x(03)00083-9

zbMATH Keywords

finite fieldsKloosterman sumsnonlinear system of equations

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Exponential sums (11T23) Gauss and Kloosterman sums; generalizations (11L05)

Related Items (4)

On a conjecture concerning Kloosterman polynomials ⋮ On cosets of weight 4 of binary BCH codes with minimum distance 8 and exponential sums ⋮ A transform property of Kloosterman sums ⋮ New Kloosterman sums identities over \(\mathbb F_{2^m}\) for all \(m\).

Cites Work

• New Kloosterman sums identities over \(\mathbb F_{2^m}\) for all \(m\).
• On \(\mathbb{Z}_4\)-linear Goethals codes and Kloosterman sums
• The weights of the orthogonals of the extended quadratic binary Goppa codes
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• On coset weight distributions of the Z/sub 4/-linear Goethals codes
• Infinite Families of 3-Designs from Z₄ -Goethals Codes with Block Size 8
• On the solution of algebraic equations over finite fields
• Kloosterman sums and finite field extensions
• Bounds for exponential sums
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