Generalized Hamming Weights of Irreducible Cyclic Codes

被引：35
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.
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页码：4905 / 4913
页数：9
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