Group structure on projective spaces and cyclic codes over finite fields

Gilles Lachaud; Isabelle Lucien; Dany-Jack Mercier; Robert Rolland

doi:10.1006/ffta.1999.0268

Journal articles

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

Domain :

Mathematics [math] / Commutative Algebra [math.AC]

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https://hal.univ-antilles.fr/hal-00770256
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Submitted on : Friday, January 4, 2013 - 6:51:19 PM
Last modification on : Tuesday, March 30, 2021 - 3:19:04 AM

Group structure on projective spaces and cyclic codes over finite fields

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Group structure on projective spaces and cyclic codes over finite fields

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