Generalized Hamming weights and some parameterized codes

被引：7

作者：

Gonzalez Sarabia, Manuel ^{[1
]}

Renteria Marquez, Carlos ^{[2
]}

机构：

[1] Inst Politecn Nacl, UPIITA, Dept Ciencias Basicas, Av IPN 2580, Mexico City 07340, DF, Mexico

[2] Inst Politecn Nacl, ESFM, Dept Matemat, Mexico City 07300, DF, Mexico

来源：

DISCRETE MATHEMATICS | 2016年 / 339卷 / 02期

关键词：

Toric set; Parameterized code; Generalized Hamming weight; Minimum distance; Embedded set; VANISHING IDEALS; GRAPHS;

D O I：

10.1016/j.disc.2015.10.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we find the complete weight hierarchy of the codes parameterized by the edges of the cycle C-4 and an upper bound in the case of the complete bipartite graph K-2,K-n. Moreover we find some bounds for the generalized Hamming weights of some codes parameterized by a set of monomials of the same degree. These bounds work in the case of codes parameterized by the edges of any simple graph G. Also we establish the relationships among the generalized Hamming weights of any parameterized code of the form C-x(d) and the generalized Hamming weights of the parameterized code of the form C-x'(d), when X' is embedded in X. (c) 2015 Elsevier B.V. All rights reserved.

引用

页码：813 / 821

页数：9

共 21 条

[1]

[Anonymous], MONOGRAPHIES U MATH

[2] On the second Hamming weight of some Reed-Muller type codes [J].

Carvalho, Cicero .

FINITE FIELDS AND THEIR APPLICATIONS, 2013, 24 :88-94

[3] Reed-Muller codes on complete intersections [J].

Duursma, IM ;

Rentería, C ;

Tapia-Recillas, H .

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2001, 11 (06) :455-462

[4] Projective parameterized linear codes [J].

Gonzalez Sarabia, Manuel ;

Renteria Marquez, Carlos ;

Sarmiento Rosales, Eliseo .

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2015, 23 (02) :223-240

[5] Parameterized Codes over Cycles [J].

Gonzalez Sarabia, Manuel ;

Lara, Joel Nava ;

Renteria Marques, Carlos ;

Sarmiento Rosales, Eliseo .

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2013, 21 (03) :241-255

[6]

Sarabia MG, 2013, MATH COMMUN, V18, P377

[7] Minimum distance of some evaluation codes [J].

Gonzalez Sarabia, Manuel ;

Renteria Marquez, Carlos ;

Sanchez Hernandez, Antonio J. .

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2013, 24 (02) :95-106

[8]

Gonzalez-Sarabia M., 2003, C NUMER, V161, P105

[9]

Grayson D., 1996, MACAULAY2

[10]

Li Zhi-min, 2011, ADV COMPUT COMMUN CO, V121, P281

← 1 2 3 →