We give a new description of Generalized Reed-Muller codes considered as ideals in a modular algebra A. But above all, we point out the link beetween both formulations. The GRM-codes, introduced by Kasami, Lin and Peterson, are a generalization of the Reed and Muller codes. At the same time, Berman has proved that RM-codes are the radical powers of A. Our construction is, in fact, a generalisation of Berman's resulf which is obtained from the Kasami and al. definition.