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

May 28, 2019 · Declared Dead · 🏛 arXiv.org

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Authors Manuel Gonzalez-Sarabia, Delio Jaramillo, Rafael H. Villarreal arXiv ID 1905.12136 Category math.AC Cross-listed cs.IT, math.AG, math.CO Citations 4 Venue arXiv.org Last Checked 1 month ago
Abstract
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 $\mathbb{X}$ 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 $\mathbb{X}$ and their dual codes in terms of the basic parameters and the generalized Hamming weights of the corresponding projective Reed--Muller-type codes on $\mathbb{X}$ and their dual codes.
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