An Open Problem on the Distribution of a Niho-Type Cross-Correlation Function

Yongbo Xia; Nian Li; Xiangyong Zeng; Tor Helleseth

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An Open Problem on the Distribution of a Niho-Type Cross-Correlation Function

机译：Niho型互相关函数的分布的一个开放问题

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摘要

In this paper, let n=2k and d=3⋅2k−2 with k≥3 and gcd(d,2n−1)=1 . Based on some analysis of certain equations over finite fields and the number of codewords with Hamming weight five in Zetterberg code, the correlation distribution between a binary m -sequence of period 2n−1 and its d -decimation sequence is completely determined. This solves a ten-year-old open problem proposed by Dobbertin et al.

机译：在本文中，设n = 2k和d =3⋅2k-2，其中k≥3和gcd（d，2n-1）= 1。通过对有限域上某些方程的分析以及Zetterberg码中汉明权重为5的码字的数目，可以确定周期2n-1的二进制m序列与其d抽取序列之间的相关分布。这解决了Dobbertin等人提出的已有十年历史的开放性问题。

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来源
《IEEE Transactions on Information Theory》 |2016年第12期|7546-7554|共9页
作者
Yongbo Xia; Nian Li; Xiangyong Zeng; Tor Helleseth;
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作者单位

Department of Mathematics and Statistics, South-Central University for Nationalities, Wuhan, China;

Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, China;

Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, China;

Department of Informatics, University of Bergen, Bergen, Norway;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Correlation; Informatics; Hamming weight; Indexes; Navigation; Radar applications;

机译：相关;信息学;权重;索引;导航;雷达应用;

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1. On Four-Valued Niho-Type Cross-Correlation Functions of $m$-Sequences [J] . Ranto K., Rosendahl P. IEEE Transactions on Information Theory . 2006,第期

机译：$ m $-序列的四值Niho型互相关函数
2. Optimal Cyclic Codes With Generalized Niho-Type Zeros and the Weight Distribution [J] . Xiong Maosheng, Li Nian Information Theory, IEEE Transactions on . 2015,第9期

机译：具有广义Niho型零点和权重分布的最佳循环码
3. Improving the shape of the cross-correlation function for leak detection in a plastic water distribution pipe using acoustic signals [J] . Gao Yan, Brennan Michael J., Liu Yuyou, Applied Acoustics . 2017,第deca期

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4. THE EFFECTS OF FILTERING ON THE SHAPE OF THE CROSS-CORRELATION FUNCTION FOR LEAK DETECTION IN PLASTIC WATER DISTRIBUTION PIPES [C] . Fabricio C. L. Almeida, Phillip Joseph, Michael Brennan, International Congress on Sound and Vibration . 2011

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An Open Problem on the Distribution of a Niho-Type Cross-Correlation Function

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