Group structure on projective spaces and cyclic codes over finite fields
Lachaud, Gilles ; Lucien, Isabelle ; Mercier, Dany-Jack ; Rolland, Robert
HAL, hal-00770256 / Harvested from HAL
Text on HAL
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.
Publié le : 2000-04-01
Classification:  reed-Muller,  cyclic codes,  error corroe corecting codes,  [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC] 
@article{hal-00770256,
     author = {Lachaud, Gilles and Lucien, Isabelle and Mercier, Dany-Jack and Rolland, Robert},
     title = {Group structure on projective spaces and cyclic codes over finite fields},
     journal = {HAL},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00770256}
}

Lachaud, Gilles; Lucien, Isabelle; Mercier, Dany-Jack; Rolland, Robert. Group structure on projective spaces and cyclic codes over finite fields. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00770256/