Designs, Codes and Cryptography

, Volume 17, Issue 1, pp 269–288

On Z4-Linear Goethals Codes and Kloosterman Sums

  • Tor Helleseth
  • Victor Zinoviev

DOI: 10.1023/A:1026491513009

Cite this article as:
Helleseth, T. & Zinoviev, V. Designs, Codes and Cryptography (1999) 17: 269. doi:10.1023/A:1026491513009


Studying the coset weight distributions of the Z4-linear Goethals codes, e connect these codes with the Kloosterman sums. From one side, e obtain for some cases, of the cosets of weight four, the exact expressions for the number of code ords of weight four in terms of the Kloosterman sums. From the other side, e obtain some limitations for the possible values of the Kloosterman sums, hich improve the well known results due to Lachaud and Wolfmann kn:lac.

Z4-linear Goethals codecoset weight distributionnonlinear system of equationsexponential sumsKloosterman sums

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Tor Helleseth
    • 1
  • Victor Zinoviev
    • 2
  1. 1.Department of InformaticsUniversity of BergenBergenNoray
  2. 2.Institute for Problems of Information Transmission of theRussian Academy of SciencesMoscoRussia