On the generalized Hamming weights of certain Reed-Muller-type codes
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There is a nice combinatorial formula of P. Beelen and M. Datta for the r-th generalized Hamming weight of an affine 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 affine 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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