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最小距离为4的最优五元循环码
Optimal quinary cyclic codes with minimum distance four
- 通信学报 2017年38卷第2期 页码：74-80
- 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：
[ "田叶（1987-），女，山西平遥人，西安电子科技大学博士生，主要研究方向为布尔函数、序列密码的分析与构造。" ]
[ "张玉清（1966-），男，陕西宝鸡人，中国科学院大学教授、博士生导师，主要研究方向为网络与信息系统安全。" ]
[ "胡予濮（1955-），男，河南濮阳人，西安电子科技大学教授、博士生导师，主要研究方向为序列密码与分组密码、网络安全协议的设计与分析。" ]
- 基金信息：国家自然科学基金资助项目(61572460);国家自然科学基金资助项目(61272481);国家重点研究计划基金资助项目(2016YFB0800703);国家发展改革委员会信息安全专项基金资助项目((2012)1424);国家111计划基金资助项目(B16037)
DOI：10.11959/j.issn.1000-436x.2017030
中图分类号： TN918-
网络出版日期：2017-02，
纸质出版日期：2017-02-25
- 稿件说明：
移动端阅览
田叶, 张玉清, 胡予濮. 最小距离为4的最优五元循环码[J]. 通信学报, 2017,38(2):74-80.
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.
田叶, 张玉清, 胡予濮. 最小距离为4的最优五元循环码[J]. 通信学报, 2017,38(2):74-80. DOI： 10.11959/j.issn.1000-436x.2017030.
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
(1
e
t)
进行研究。首先，给出一种有效且快速判断五元循环码C
(1
e
t)
是否最优的方法；其次，基于提出的方法得到当e=5
k
+1及e=5
m
−2时，循环码C
(1
e
t)
为最优循环码；最后，基于有限域
<math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>5</mn> <mi>m</mi> </msup> </mrow> </msub> </math>
中的完全非线性函数，构造一类具有参数[5
m
−1
5
m
−2m−2
4
]
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
(1
e
t)
were optimal codes was obtained.Secondly
based on the proposed method
when the equation e=5
k
+1 or e=5
m
−2hold
the theorem that the cyclic codes C
(1
e
t)
were optimal quinary cyclic codes was proved.In addition
perfect nonlinear monomials were used to construct optimal quinary cyclic codes with parameters[5
m
−1
5
m
−2m−2
4
]
optimal quinary cyclic codes over
<math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>5</mn> <mi>m</mi> </msup> </mrow> </msub> </math>
.
关键词
Keywords
references
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