Abstract :
For generalized Reed–Muller, GRM(q,d,n), codes, the determination of the second weight is still generally unsolved, it is an open question of Cherdieu and Rolland [J.P. Cherdieu, R. Rolland, On the number of points of some hypersurfaces in , Finite Fields Appl. 2 (1996) 214–224]. In order to answer this question, we study some maximal hypersurfaces and we compute the second weight of GRM(q,d,n) codes with the restriction that q 2d.
