Optimal quinary cyclic codes with minimum distance four

Ye TIAN; Yu-qing ZHANG; Yu-pu HU

doi:10.11959/j.issn.1000-436x.2017030

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Optimal quinary cyclic codes with minimum distance four

Papers | 更新时间：2024-06-05

- Optimal quinary cyclic codes with minimum distance four
- Journal on Communications Vol. 38, Issue 2, Pages: 74-80(2017)
- 作者机构：
  
  1. 西安电子科技大学综合业务网理论及关键技术国家重点实验室，陕西西安 710071
  2. 中国科学院大学国家计算机网络入侵防范中心，北京 101408
- 作者简介：
- 基金信息：
  
  The National Natural Science Foundation of China(61572460);The National Natural Science Foundation of China(61272481);The National Key Research and Development Project(2016YFB0800703);The National Information Security Special Projects of National Development,The Reform Commission of China((2012)1424);China 111 Project(B16037)
- DOI：10.11959/j.issn.1000-436x.2017030
  CLC： TN918
- Online First：2017-02，
  
  Published：25 February 2017
- 稿件说明：
移动端阅览
Ye TIAN, Yu-qing ZHANG, Yu-pu HU. Optimal quinary cyclic codes with minimum distance four[J]. Journal on Communications, 2017, 38(2): 74-80.
DOI：

Ye TIAN, Yu-qing ZHANG, Yu-pu HU. Optimal quinary cyclic codes with minimum distance four[J]. Journal on Communications, 2017, 38(2): 74-80. DOI： 10.11959/j.issn.1000-436x.2017030.

摘要

循环码是线性分组码中最重要的一个子类，由于其具有代数结构清晰、编译码简单且易于实现，被广泛地应用于通信系统和储存设备中。目前，大部分已有的研究工作最多只能实现三元最优循环码，对五元循环码的研究工作较少。对一类五元最优循环码C

进行研究。首先，给出一种有效且快速判断五元循环码C

是否最优的方法；其次，基于提出的方法得到当e=5

+1及e=5

−2时，循环码C

为最优循环码；最后，基于有限域

中的完全非线性函数，构造一类具有参数[5

−1

−2m−2

]

的五元最优循环码。

Abstract

Cyclic codes are an extremely important subclass of linear codes.They are widely used in the communication systems and data storage systems because they have efficient encoding and decoding algorithm.Until now

how to construct the optimal ternary cyclic codes has received a lot of attention and much progress has been made.However

there is less research about the optimal quinary cyclic codes.Firstly

an efficient method to determine if cyclic codes C

were optimal codes was obtained.Secondly

based on the proposed method

when the equation e=5

+1 or e=5

−2hold

the theorem that the cyclic codes C

were optimal quinary cyclic codes was proved.In addition

perfect nonlinear monomials were used to construct optimal quinary cyclic codes with parameters[5

−1

−2m−2

]

optimal quinary cyclic codes over

关键词

Keywords

references

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