Abstract
We present a description of abelian codes by means of a trace function. This new description leads to an estimation of the weights of these codes that generalizes results of Baumert, McEliece and Niederreiter about the weights of cyclic codes.
Similar content being viewed by others
References
L. D. Baumert and R. J. McEliece, Weights of irreducible cyclic codes, Information and Control, Vol. 20 (1976) pp. 158-175.
A. Blanchard, Les corps non commutatifs, Presses Universitaires de France, Vendome (1972).
C.W. Curtis and I. Reiner, Representation of Finite Groups and Associative Algebras, Wiley Classics Library, New York (1962).
R. Lidl and H. Niederreiter, Finite Fields, volume 20, Addison-Wesley-Reading, MA (1983).
F. J. Macwilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam (1977).
H. Niederreiter, Weights of cyclic codes, Inform. and Control, Vol. 34, No.2 (1977) pp. 130-140.
J.-P. Serre, Représentations Linéaires des Groupes Finis, Hermann, Paris (1967).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Langevin, P. Weights of Abelian Codes. Designs, Codes and Cryptography 14, 239–245 (1998). https://doi.org/10.1023/A:1008252803758
Issue Date:
DOI: https://doi.org/10.1023/A:1008252803758