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

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...

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Bibliographic Details
Published in:arXiv.org 2019-07
Main Authors: Gonzalez-Sarabia, Manuel, Jaramillo, Delio, Villarreal, Rafael H
Format: Article
Language:English
Subjects:
Combinatorial analysis
Fields (mathematics)
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Summary: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.
ISSN:2331-8422