SOME NEW CLASSES OF CYCLIC CODES WITH THREE OR SIX WEIGHTS

被引:2
|
作者
Xia, Yongbo [1 ]
Helleseth, Tor [2 ]
Li, Chunlei [3 ]
机构
[1] South Central Univ Natl, Dept Math & Stat, Wuhan 430074, Peoples R China
[2] Univ Bergen, Dept Informat, N-5020 Bergen, Norway
[3] Univ Stavanger, Dept Elect Engn & Comp Sci, CIPSI, N-4036 Stavanger, Norway
基金
中国国家自然科学基金;
关键词
Cyclic code; weight distribution; exponential sum; quadratic form; CROSS-CORRELATION; DISTRIBUTIONS; SEQUENCES;
D O I
10.3934/amc.2015.9.23
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
In this paper, a class of three-weight cyclic codes over prime fields IF p of odd order whose duals have two zeros, and a class of six-weight cyclic codes whose duals have three zeros are presented. The weight distributions of these cyclic codes are derived.
引用
收藏
页码:23 / 36
页数:14
相关论文
共 50 条
  • [1] Several Classes of Cyclic Codes With Either Optimal Three Weights or a Few Weights
    Heng, Ziling
    Yue, Qin
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2016, 62 (08) : 4501 - 4513
  • [2] ON SOME CLASSES OF CODES WITH A FEW WEIGHTS
    Liu, Yiwei
    Liu, Zihui
    ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2018, 12 (02) : 415 - 428
  • [3] THE PUNCTURED CODES OF TWO CLASSES OF CYCLIC CODES WITH FEW WEIGHTS
    Ji, Qinqin
    Zheng, Dabin
    Wang, Xiaoqiang
    ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2022, 16 (04) : 791 - 810
  • [4] Three classes of linear codes with two or three weights
    Heng, Ziling
    Yue, Qin
    Li, Chengju
    DISCRETE MATHEMATICS, 2016, 339 (11) : 2832 - 2847
  • [5] ON THE GENERALIZED HAMMING WEIGHTS OF SEVERAL CLASSES OF CYCLIC CODES
    FENG, GL
    TZENG, KK
    WEI, VK
    IEEE TRANSACTIONS ON INFORMATION THEORY, 1992, 38 (03) : 1125 - 1130
  • [6] NEW CONSTRUCTIONS OF SYSTEMATIC AUTHENTICATION CODES FROM THREE CLASSES OF CYCLIC CODES
    Liu, Yunwen
    Qu, Longjiang
    Li, Chao
    ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2018, 12 (01) : 1 - 16
  • [7] On three weights in cyclic codes with two zeros
    McGuire, G
    FINITE FIELDS AND THEIR APPLICATIONS, 2004, 10 (01) : 97 - 104
  • [8] Two Classes of Linear Codes with Two or Three Weights
    Xu, Guangkui
    Cao, Xiwang
    Gao, Jian
    Luo, Gaojun
    IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2018, E101A (12): : 2366 - 2373
  • [9] Generalized Hamming weights of three classes of linear codes
    Jian, Gaopeng
    Feng, Rongquan
    Wu, Hongfeng
    FINITE FIELDS AND THEIR APPLICATIONS, 2017, 45 : 341 - 354
  • [10] Some Classes of Mixed Alphabet Codes With Few Weights
    Wu, Rongsheng
    Shi, Minjia
    IEEE COMMUNICATIONS LETTERS, 2021, 25 (05) : 1431 - 1434