The Weight Hierarchy of Some Reducible Cyclic Codes

被引：16

作者：

Xiong, Maosheng ^{[1
]}

Li, Shuxing ^{[2
]}

Ge, Gennian ^{[3
,4
]}

机构：

[1] Hong Kong Univ Sci & Technol, Dept Math, Hong Kong, Hong Kong, Peoples R China

[2] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China

[3] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China

[4] Beijing Ctr Math & Informat Interdisciplinary Sci, Beijing 100048, Peoples R China

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2016年 / 62卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Cyclic code; exponential sum; generalized Hamming weight; weight hierarchy; GENERALIZED HAMMING WEIGHTS; UPPER-BOUNDS; BCH CODES; 2ND; COMPLEXITY; PRODUCTS; CURVES;

D O I：

10.1109/TIT.2016.2570236

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 (GHWs) of linear codes are fundamental parameters, the knowledge of which is of great interest in many applications. However, to determine the GHWs of linear codes is difficult in general. In this paper, we study the GHWs for a family of reducible cyclic codes and obtain the complete weight hierarchy in several cases. This is achieved by extending the idea of Yang et al. into higher dimension and by employing some interesting combinatorial arguments. It shall be noted that these cyclic codes may have arbitrary number of nonzeros.

引用

页码：4071 / 4080

页数：10

共 60 条

[1]

[Anonymous], 1983, Encyclopedia Math. Appl.

[2] New upper bounds on generalized weights [J].

Ashikhmin, A ;

Barg, A ;

Litsyn, S .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1999, 45 (04) :1258-1263

[3] The weight hierarchy of Hermitian codes [J].

Barbero, AI ;

Munuera, C .

SIAM JOURNAL ON DISCRETE MATHEMATICS, 2000, 13 (01) :79-104

[4] New Lower Bounds on the Generalized Hamming Weights of AG Codes [J].

Bras-Amoros, Maria ;

Lee, Kwankyu ;

Vico-Oton, Albert .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2014, 60 (10) :5930-5937

[5] THE GEOMETRY OF 2-WEIGHT CODES [J].

CALDERBANK, R ;

KANTOR, WM .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1986, 18 :97-122

[6]

Cary Huffman., 2003, Fundamentals of Error-Correcting Codes

[7] On generalized hamming weights of binary primitive BCH codes with minimum distance one less than a power of two [J].

Cheng, J ;

Chao, CC .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1997, 43 (01) :294-299

[8] On the generalized weights of a class of trace codes [J].

Cherdieu, JP ;

Mercier, DJ ;

Narayaninsamy, T .

FINITE FIELDS AND THEIR APPLICATIONS, 2001, 7 (02) :355-371

[9]

CHUNG H, 1991, LECT NOTES COMPUT SC, V539, P118

[10] UPPER-BOUNDS ON GENERALIZED DISTANCES [J].

COHEN, G ;

LITSYN, S ;

ZEMOR, G .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1994, 40 (06) :2090-2092

← 1 2 3 4 5 6 →