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

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

doi:10.2478/auom-2020-0014

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 28 (2020): Issue 1 (March 2020)

By: Manuel González-Sarabia, Delio Jaramillo and Rafael H. Villarreal

Open Access

|Apr 2020

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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Articles in this issue

DOI: https://doi.org/10.2478/auom-2020-0014 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 205 - 217

Submitted on: May 29, 2019

Accepted on: Jul 15, 2019

Published on: Apr 9, 2020

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Reed-Muller-type codes,

generalized Hamming weights,

Related subjects:

© 2020 Manuel González-Sarabia, Delio Jaramillo, Rafael H. Villarreal, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 28 (2020): Issue 1 (March 2020)