<abstract xmlns="http://www.w3.org/1999/xhtml"><p>There is a nice combinatorial formula of P. Beelen and M. Datta for the <italic>r</italic>-th generalized Hamming weight of an a ne cartesian code. Using this combinatorial formula we give an easy to evaluate formula to compute the <italic>r</italic>-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.</p></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.

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On the generalized Hamming weights of certain Reed\u2013Muller-type codes"}

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...

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

Published Online: Apr 09, 2020

Page range: 205 - 217

Received: May 29, 2019

Accepted: Jul 15, 2019

DOI: https://doi.org/10.2478/auom-2020-0014

Keywords
Reed-Muller-type codes, generalized Hamming weights, linear code, Veronese code

© 2020 Manuel González-Sarabia et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Apr 09, 2020

Page range: 205 - 217

Received: May 29, 2019

Accepted: Jul 15, 2019

DOI: https://doi.org/10.2478/auom-2020-0014

KeywordsReed-Muller-type codes, generalized Hamming weights, linear code, Veronese code

© 2020 Manuel González-Sarabia et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Reed-Muller-type codes, generalized Hamming weights, linear code, Veronese code