Group structure on projective spaces and cyclic codes over finite fields

Gilles Lachaud 1, * Isabelle Lucien 2 Dany-Jack Mercier 2, 3 Robert Rolland 1
* Corresponding author
1 IML - Institut de mathématiques de Luminy
2 Equipe Applications de l'Algèbre et de l'Arithmétique
D.M.I. - Département de Mathématiques et Informatique
3 IUFM Guadeloupe - Institut universitaire de formation des maîtres - Guadeloupe
Abstract : We study the geometrical properties of the subgroups of the multiplicative group of a finite extension of a finite field endowed with its vector space structure, and we show that in some cases the associated projective space has a natural groupe structure. We construct some cyclic codes related to Reed-Muller codes by evaluating polynomials on these subgroups. The geometrical properties of these groups give a fairly simple description of these codes of the Reed-Muller kind.
Keywords : reed-Muller cyclic codes error corroe corecting codes
Document type :
Journal articles
Complete list of metadatas
https://hal.univ-antilles.fr/hal-00770256
Contributor : Pamphile Isch <>
Submitted on : Friday, January 4, 2013 - 6:51:19 PM
Last modification on : Saturday, December 14, 2019 - 1:24:02 PM

Links full text

openaccess

Identifiers

Collections

UNIV-AG | CNRS | INSMI | UNIV-AMU | IML | I2M

Citation

Gilles Lachaud, Isabelle Lucien, Dany-Jack Mercier, Robert Rolland. Group structure on projective spaces and cyclic codes over finite fields. Finite Fields and Their Applications, Elsevier, 2000, 6 (2), pp.119-129. ⟨10.1006/ffta.1999.0268⟩. ⟨hal-00770256⟩

Export

BibTeX TEI DC DCterms EndNote

Share

Metrics

Record views

308

Contact

Informations

CCSD