On the generalized Hamming weights of certain Reed–Muller-type codes
Manuel González Sarabia, Delio Jaramillo-Velez, Rafael H. Villarreal · Analele Universităţii "Ovidius" Constanţa. Seria Matematică · 2020
Abstract There is a nice combinatorial formula of P. Beelen and M. Datta for the r -th generalized Hamming weight of an a ne cartesian code. Using this combinatorial formula we give an easy to evaluate formula to compute the r -th generalized Hamming weight for a family of a ne cartesian codes. If 𝕏 is a set of projective points over a finite field we determine the basic parameters and the generalized Hamming weights of the Veronese type codes on 𝕏 and their dual codes in terms of the basic parameters and the generalized Hamming weights of the corresponding projective Reed–Muller-type codes on 𝕏 and their dual codes.