Generalized Hamming Weights of Irreducible Cyclic Codes

被引：34

作者：

Yang, Minghui ^{[1
]}

Li, Jin ^{[2
]}

Feng, Keqin ^{[3
]}

Lin, Dongdai ^{[1
]}

机构：

[1] Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China

[2] Hefei Univ Technol, Sch Math, Hefei 230001, Peoples R China

[3] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2015年 / 61卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Generalized Hamming weight; irreducible cyclic code; Gauss sum; GEOMETRIC GOPPA CODES; HERMITIAN CODES; LINEAR CODES; BCH CODES; HIERARCHY; BOUNDS;

D O I：

10.1109/TIT.2015.2444013

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The generalized Hamming weights d(r)(C) of a linear code C are a natural generalization of the minimum Hamming distance d(C)[= d(1)(C)] and have become an important research object in coding theory since Wei's originary work in 1991. In this paper, two general formulas on d(r) (C) for irreducible cyclic codes are presented using Gauss sums and the weight hierarchy {d(1)(C), d(2)(C), ... , d(k)(C)} (k = dim C) is completely determined for several cases.

引用

页码：4905 / 4913

页数：9

共 50 条

[31] A note on the generalized Hamming weights of Reed–Muller codes
Peter Beelen
Applicable Algebra in Engineering, Communication and Computing, 2019, 30 : 233 - 242
[32] Weight functions and generalized hamming weights of linear codes
Nogin D.Yu.
Problems of Information Transmission, 2005, 41 (2) : 91 - 104
[33] The second and third generalized Hamming weights of Hermitian codes
Munuera, C
Ramirez, D
IEEE TRANSACTIONS ON INFORMATION THEORY, 1999, 45 (02) : 709 - 712
[34] Relative generalized Hamming weights of affine Cartesian codes
Mrinmoy Datta
Designs, Codes and Cryptography, 2020, 88 : 1273 - 1284
[35] A class of cyclotomic linear codes and their generalized Hamming weights
Li, Fei
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2018, 29 (06) : 501 - 511
[36] On the Generalized Hamming Weights of (r, δ)-Locally Repairable Codes
Hao, Jie
Chen, Bin
IEEE ACCESS, 2020, 8 (08): : 149706 - 149713
[37] Improvements on generalized hamming weights of some trace codes
Güneri, C
Özbudak, F
DESIGNS CODES AND CRYPTOGRAPHY, 2006, 39 (02) : 215 - 231
[38] A class of cyclotomic linear codes and their generalized Hamming weights
Fei Li
Applicable Algebra in Engineering, Communication and Computing, 2018, 29 : 501 - 511
[39] On Generalized Hamming Weights for Galois Ring Linear Codes
Ashikhmin A.
Designs, Codes and Cryptography, 1998, 14 (2) : 107 - 126
[40] Improvements on Generalized Hamming Weights of Some Trace Codes
Cem Güneri
Ferruh Özbudak
Designs, Codes and Cryptography, 2006, 39 : 215 - 231

← 1 2 3 4 5 →