Optimal Quinary Cyclic Codes with Minimum Distance Four

被引：0
作者：
FAN Jinmei [1 ]
ZHANG Yanhai [1 ]
机构：
[1] College of Science, Guilin University of Technology
来源：
Chinese Journal of Electronics | 2020年 / 29卷 / 03期
关键词：
Finite field; Cyclic code; Irreducible polynomial; Monomial;
D O I：
暂无
中图分类号：
O157.4 [编码理论（代数码理论）];
学科分类号：
070104 ;
摘要：
The necessary and sufficient condition for the quinary cyclic codes with generator polynomial（x+1）m;（x）m;e（x） to have parameters [5;-1, 5;-2m-2, 4]is provided by analyzing solutions of certain equations over the finite field F;. And thus several classes of new optimal quinary cyclic codes with the same parameters and generator polynomial are constructed based on analyzing irreducible factors of certain polynomials with low degrees over finite fields.
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收藏
页码：515 / 524
页数：10
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共 8 条
  • [1] Two families of Niho sequences having four-valued cross correlation with m-sequences
    Fan, JinMei
    Xu, YunGe
    Xia, YongBo
    Zeng, XiangYong
    [J]. SCIENCE CHINA-MATHEMATICS, 2017, 60 (12) : 2377 - 2390
  • [2] A class of optimal ternary cyclic codes and their duals[J] . Cuiling Fan,Nian Li,Zhengchun Zhou.Finite Fields and Their Applications . 2016
  • [3] Optimal ternary cyclic codes with minimum distance four and five[J] . Nian Li,Chunlei Li,Tor Helleseth,Cunsheng Ding,Xiaohu Tang.Finite Fields and Their Applications . 2014
  • [4] A triple-error-correcting cyclic code from the Gold and Kasami–Welch APN power functions[J] . Xiangyong Zeng,Jinyong Shan,Lei Hu.Finite Fields and Their Applications . 2011 (1)
  • [5] Power functions with low uniformity on odd characteristic finite fields[J] . ZhengBang Zha,XueLi Wang.Science China Mathematics . 2010 (8)
  • [6] The weight distribution of a class of p -ary cyclic codes[J] . Xiangyong Zeng,Lei Hu,Wenfeng Jiang,Qin Yue,Xiwang Cao.Finite Fields and Their Applications . 2009 (1)
  • [7] Planar Functions and Planes of Lenz-Barlotti Class II
    Coulter R.S.
    Matthews R.W.
    [J]. Designs, Codes and Cryptography, 1997, 10 (2) : 167 - 184
  • [8] PLANES OF ORDER N WITH COLLINEATION GROUPS OF ORDER N2
    DEMBOWSKI, P
    OSTROM, TG
    [J]. MATHEMATISCHE ZEITSCHRIFT, 1968, 103 (03) : 239 - &
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