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
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
收藏
页码:202 / 224
页数:23
相关论文
共 24 条
[11]  
Lidl R., 1983, Finite fields, Encyclopedia of Mathematics and its Applications, V20
[12]   On the Weight Distributions of Two Classes of Cyclic Codes [J].
Luo, Jinquan ;
Feng, Keqin .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2008, 54 (12) :5332-5344
[13]   The Weight Enumerator of a Class of Cyclic Codes [J].
Ma, Changli ;
Zeng, Liwei ;
Liu, Yang ;
Feng, Dengguo ;
Ding, Cunsheng .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2011, 57 (01) :397-402
[14]  
Mac Williams F.J., 1997, THEORY ERROR CORRECT
[15]   On three weights in cyclic codes with two zeros [J].
McGuire, G .
FINITE FIELDS AND THEIR APPLICATIONS, 2004, 10 (01) :97-104
[16]   A Family of Two-Weight Irreducible Cyclic Codes [J].
Rao, Asha ;
Pinnawala, Nimalsiri .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2010, 56 (06) :2568-2570
[17]  
Trachtenberg H.M., 1970, Ph.D. dissertation
[18]   The Weight Distribution of an Extended Class of Reducible Cyclic Codes [J].
Vega, Gerardo .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2012, 58 (07) :4862-4869
[19]   The weight distributions of a class of cyclic codes III [J].
Xiong, Maosheng .
FINITE FIELDS AND THEIR APPLICATIONS, 2013, 21 :84-96
[20]   The weight distribution of a class of linear codes from perfect nonlinear functions [J].
Yuan, J ;
Carlet, C ;
Ding, C .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (02) :712-717