Abstract
We introduce a special basis for the description of the primitive extended cyclic codes, considered as subspaces of the modular algebra A=GF(pm)[GF(pm)]. Using properties of this basis, we determine the automorphism group of some extended cyclic codes, among the extended Reed Solomon codes.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
T.Berger & P.Charpin The automorphism group of the generalized Reed Muller codes Rapport INRIA, to appear.
T.Berger Sur le groupe d'automorphismes des codes cycliques étendus primitifs affine-invariants Thèse de l'Université de Limoges, in preparation.
P.Charpin The extended Reed Solomon codes considered as ideals of a modular algebra Annals of Discrete Mathematics. 17(1983)171.176.
P.Charpin Codes cycliques étendus invariants sous le groupe affine Thèse de Doctorat d'Etat, Université Paris VII, LITP (1987).
A.Dür The automorphism group of Reed Solomon codes J. of Combinatorial Theory, serie A, vol.44, no1 (1987).
T. Kasami, S. Lin &W.W. Peterson Some results on cyclic codes which are invariant under the affine group and their applications Info. and Control, vol 11, p475–496 (1967).
F.J.Macwilliams & N.J.A.Sloane The theory of error correcting codes North-Holland (1986).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Berger, T. (1991). A direct proof for the automorphism group of reed solomon codes. In: Cohen, G., Charpin, P. (eds) EUROCODE '90. EUROCODE 1990. Lecture Notes in Computer Science, vol 514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54303-1_114
Download citation
DOI: https://doi.org/10.1007/3-540-54303-1_114
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54303-9
Online ISBN: 978-3-540-47546-0
eBook Packages: Springer Book Archive