On the generalized Hamming weights of certain Reed–Muller-type codes

González-Sarabia, Manuel; Jaramillo, Delio; Villarreal, Rafael H.

doi:10.2478/auom-2020-0014

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.

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On the generalized Hamming weights of certain Reed–Muller-type codes

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