On the generalized Hamming weights of certain Reed–Muller-type codes-Reference-Cited by-同舟云学术

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

Published:2020-03-01 Issue:1 Volume:28 Page:205-217
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

González-Sarabia Manuel¹,Jaramillo Delio²,Villarreal Rafael H.³

Affiliation:

1. Instituto Politécnico Nacional , UPIITA, Av. IPN No. 2580, Col. Barrio la Laguna, Ticomán, Gustavo A. Madero, C.P. 07340, Ciudad de México , México . Departamento de Ciencias Básicas . Supported by COFAA-IPN and SNI, México .

2. Departamento de Matemáticas , Centro de Investigación y de Estudios Avanzados del IPN , Apartado Postal 14–740, 07000 Mexico City, D.F. Supported by a scholarship from CONACyT, México .

3. Departamento de Matemáticas , Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14–740, 07000 Mexico City, D.F. Supported by SNI, México .

Abstract

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/auom-2020-0014

Reference31 articles.

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