The weight distributions of two classes of p-ary cyclic codes

被引：18

作者：

Zheng, Dabin ^{[1
]}

Wang, Xiaoqiang ^{[1
]}

Hu, Lei ^{[2
,3
]}

Zeng, Xiangyong ^{[1
,2
]}

机构：

[1] Hubei Univ, Fac Math & Stat, Wuhan 430062, Peoples R China

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

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

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2014年 / 29卷

基金：

中国国家自然科学基金;

关键词：

Cyclic code; Weight distribution; Exponential sum; Quadratic form;

D O I：

10.1016/j.ffa.2014.05.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let p be an odd prime, and m, k be positive integers with m >= 3k. Let C-1 and C-2 be cyclic codes over F-p with parity-check polynomials h(2)(x)h(3)(x) and h(1)(x)h(2)(x)h(3)(x), respectively, where h(1)(x), h(2)(x) and h(3)(x) are the minimal polynomials of gamma(-1), gamma(-(pk+1)) and gamma(-(p3k+l)) over F-p, respectively, for a primitive element gamma of F-pm. Recently, Zeng et al. (2010) obtained the weight distribution of C-2 for m/gcd(m,k) being odd. In this paper, we determine the weight distribution of C-1, and the weight distribution of C-2 for the case that m/gcd(m,k) is even. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：202 / 224

页数：23

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